Showing posts with label lagrangian. Show all posts
Showing posts with label lagrangian. Show all posts

Friday, November 18, 2016

The Flow In our Lives


In positive psychology, flow, also known as the zone, is the mental state of operation in which a person performing an activity is fully immersed in a feeling of energized focus, full involvement, and enjoyment in the process of the activity. In essence, flow is characterized by complete absorption in what one does. Named by Mihály Csíkszentmihályi, the concept has been widely referenced across a variety of fields (and has an especially big recognition in occupational therapy), though the concept has existed for thousands of years under other guises, notably in some Eastern religions.[1] Achieving flow is often colloquially referred to as being in the zone.
Flow shares many characteristics with hyperfocus. However, hyperfocus is not always described in a positive light. Some examples include spending "too much" time playing video games or getting side-tracked and pleasurably absorbed by one aspect of an assignment or task to the detriment of the overall assignment. In some cases, hyperfocus can "capture" a person, perhaps causing them to appear unfocused or to start several projects, but complete few.  Flow (psychology)

The standard definition seems to be lacking for me in terms of the experience as that flow had come to me with meaning. At its most deepest levels the experience had an alignment with all aspects of my experiences in life, as if lead to it. These pathways,  as if by laying all these lines over top one another according to an arrow of time.  It is where all these lines crossed.

While on the larger scale of experience, an objectification of actions, at the same time a subjective interpretation, becomes a pathway of expression of experiencing. This to me was like seeing qualitative equations underlying our expression of the words and experiences according too. An geometrical expression of the human experience. That, if one goes backward to a source, it would be like becoming in touch with this stream.....the flow that one touches, as if dipping a finger into the current described as the flow of life....the energy of our life expression. Once connected,  totally immersed.

I talked about this with regard to a fighting aspect in hand to hand, as a momentum felt in a circular motion, as if one used to propel this momentum through a continued force of expression. I saw this in light of Lagrangian understanding as using this to propel satellites further onward to other planets.



 In terms of Lagrangian, one is looking for the least resistance....to see that life expression always finds the fastest route and as fleeting as Deja Vu human perception is capable of perceiving that time frame.

 One has to find this subjective location in life as toward one understanding where these lines cross.  You would understand that it allows for such a pathway to have expressed itself as the life experience.

 In another form of expression I see this flow, as a connection to the arrow of time, as one would regard confirmation of life according to its enforcement as  in the deja Vu experience. One would think a predetermination as a loss in will, but this is contrary to not living our life plan as we had choose it. So one can see, how a choice was made to enter here into this life experience.....and that we choose other routes willingly

 Psychology(flow) had quite a list, and one of those stood out was the poetry.....as if to be consumed by the rise and fall of the rhythms inherent in the words of expression.  Again at the most deepest levels of these are as a subjective experience, that becomes a undifferentiated of any other.
 

Friday, December 12, 2014

The Lagrangian Configuration Box

  "Gravitation is not responsible for people falling in love. Albert Einstein"
 Of course I look a Einstein's statement here and I am perplexed as one might distance them self from the subject of gravity to see that such a comparison as I list below can run contradictory to Einstein's rule? But when considering the context of "emotive valence" as a subject worthy of the innovative materialist design products,  I consider the physiological application that emotive valence might have in understanding our world today.

Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems. It is also called molecular quantum mechanics.
When one moves through the subject of quantum biology one is lead toward the chemistry of life so as to see this trend toward understanding the conversion process that can take place as to the quantum effects as seen in quantum biology.

  The science and history of the minimal length has now been covered in a recent book by Amit Hagar:


 The Planck limits may cause a researcher to ask what particulars may be seen within reason toward the larger picture? If something is discrete in its measure then what would such particularization mean in terms of a wave?

 Several questions about consciousness must be resolved in order to acquire a full understanding of it. These questions include, but are not limited to, whether being conscious could be wholly described in physical terms, such as the aggregation of neural processes in the brain. If consciousness cannot be explained exclusively by physical events, it must transcend the capabilities of physical systems and require an explanation of nonphysical means. For philosophers who assert that consciousness is nonphysical in nature, there remains a question about what outside of physical theory is required to explain consciousness. See: The Hard Problem of Consciousness

Unification of gravity and the electrical forces may have some profound insight as too, the unification possibility that such a design could bring an understanding of logic and emotive forces. I believe,  which must be brought to bear on understanding the whole being/body? Understanding each individual's Truth. An Effective Field Theory of Emotion?

 Gravimetry is the measurement of the strength of a gravitational field.


The conversion process was self explanatory in terms of the energy consideration as to the particularity of the universe? So we look at the world in different way.

 (The CIE 1931 colour space chromaticity diagram with wavelengths in nanometers. The colours depicted depend on the colour space of the device on which the image is viewed.) International Commission on Illumination

Consider this for a moment. What may be defined as dimensional attributes, is a conversion process of the "emotive application" that I am moving toward, may have some has relevance in the affective decisions we have? I've based this on how we can see the universe in terms of Lagrangian?

A contour plot of the effective potential due to gravity and the centrifugal force of a two-body system in a rotating frame of reference. The arrows indicate the gradients of the potential around the five Lagrange points—downhill toward them (red) or away from them (blue). Counterintuitively, the L4 and L5 points are the high points of the potential. At the points themselves these forces are balanced.


On a classical scale its influence regarding the three body problem, allows one to see "variations of the gravity field" between these bodies?



Animation showing the relationship between the five Lagrangian points (red) of a planet (blue) orbiting a star (yellow), and the gravitational potential in the plane containing the orbit (grey surface with purple contours of equal potential). The potential was computed in POV-Ray using


 For fun apply a color scale to this view? You use a "configuration box" that if applied to some color scale has value in that "such points within the relationship of the three body detail aspects of the nature of this gravity?" So think about this comparison for a moment.

 We know that colour is a psychophysical experience of an observer which changes from observer to observer and is therefore impossible to replicate absolutely. In order to quantify colour in meaningful terms we must be able to measure or represent the three attributes that together give a model of colour perception. i.e. light, object and the eye. All these attributes have been standardised by the CIE or Commission Internationale de l'Eclairage. The colours of the clothes we wear and the textiles we use in our homes must be monitored to ensure that they are correct and consistent. Colour measurement is therefore essential to put numbers to colour in order to remove physical samples and the interpretation of results.See: Colour measuring equipment 

Thursday, August 07, 2014

Rosetta's arrival at comet 67P/C-G



Highlights from ESA's mission control centre during Rosetta's arrival at comet 67P/C-G on 6 August 2014. Includes live updates from the Rosetta flight control team, confirmation of orbit entry and presentation of latest images and science results.See: Rosetta arrival highlights


See Also: Rosetta Rendezvous with a Comet

Thursday, May 08, 2014

Death is Not Final

You all have to know the hammer analogy was made aware to me about a week before this debate took place. Also,  a YouTube label given to this demonstration was posted under "gaming" so I find that kind of funny given the seriousness of this debate.



I pushed Number 1.  But, you also know my bias right so I did not think providing this image would hurt in an way given that you already have some insight into my perspective? My opinion at Sean's Blog as well pertaining to this subject.

So as I am going through the debate I thought it necessary to keep a running tab for my self so as to see from what position one is speaking.  So now that I know Sean is speaking from a Naturalist point of view. I will continue.

A metaphysics that goes beyond the commitments of science is simply unsupported by the best available evidence.[27]
—Lynne Rudder Baker, Naturalism and the First-Person Perspective

 A naturalistic methodology (sometimes called an "inductive theory of science") has its value, no doubt.... I reject the naturalistic view: It is uncritical. Its upholders fail to notice that whenever they believe to have discovered a fact, they have only proposed a convention. Hence the convention is liable to turn into a dogma. This criticism of the naturalistic view applies not only to its criterion of meaning, but also to its idea of science, and consequently to its idea of empirical method.
— Karl R. Popper, The Logic of Scientific Discovery, (Routledge, 2002), pp. 52–53, ISBN 0-415-27844-9.

Okay I am at 36:58 of the video so I have had the opportunity to listen to the four speakers. I have to say oh my gosh, there is a lot here to consider, and a lot I have already considered. So I need to respond to that first part of the video.

As life calls us to do our things in the day to day, I also have a schedule today, so this posting will be broken up in terms of my response as to the first part of the video. Please be patient. It also gives me time to think about what has been said.

I want to open with the quote Sean responded too, of Eben Alexanders of Einstein. So give me time to drawn this comment out of Eben's book.

A man should look for what is, and not for what he thinks  should be. -Albert Einstein (1879-1955)

I am still ay 36:58 so I needed to finish what  what I have surmised in that first part so I can go on with the video. Below is something that I had written to my Aunt,  so hope she is okay with me repeating it here.  You will see that entry below. It basically sums up the first part of the debate for me.

As I was finishing listening to Steven Novella speak, the quote of Einstein, now gotten from Eben's book, Proof of Heaven under Prologue,  and response given by Sean Carroll was a matter of fact to the whole first part to me as it was for Sean to Eben's Alexanders use of the quote.

Something also interesting to me was Sean's admittance of wanting to believe (that death is not final) but at this point not being able too.That said a lot to me, and in the aspect of being a scientist,  I believe what he is saying.:) So I will continue on with the rest of the video now.

***
 In a note to my Aunt.

Hi Aunt Celine,

 I am a bit of a science buff when it comes to what is currently happening in science. I too had been reading about the NDE for quite a long time as well. Moody agrees with you, about science not quite ready. Since I have studied other aspects of consciousness research, it is my hope that one day we will understand this debate, as a recognition of who we all are as spiritual beings, in a physical body.

What Moody proposes is the beginning of a true dialogue based on logic and reason, and these stem from philosophy. So it is important to see the discussion in terms of where this dialogue can truly begin. Moody mentions pseudoscience and from that, his journey through philosophy. He is trying to set up a credible debate.

 I read Eben Alexander's book as well so I knew where he was coming from, as well I have been following Sean Carroll's science for sometime now. The only one that was sort of new to me was that Steve Novella, and as a neuroscientist, I am open to what he has to say. I must say then I am also a bit of philosopher that has had me venturing through aspect and developments about the Mind/ body debate that is going on, and that is where the science is saying that it is based on materialism. On my own, I have studied Plato and other philosophers.

 In order to accept materialism one has to believe, that consciousness is derived from the brain, while the other perspective is that the brain in my view, is what consciousness uses while the body is alive, but that consciousness can exist, once our body dies. That understanding is in contradiction to what science saids today, but I am saying to science, that they indeed do not have all the facts to make this conclusion even though they can simulate experience from manipulating the physical aspects of the body to produce the near death experience.

Religion has not helped me and I must say, that my upbringing within the Catholic Church has left much for me say, about its patriarchal construct, and how it falls short of providing support for what spiritual means to me. I hope you are not offended.

I do believe in a higher power, and I do believe that Heaven is capable in all of us now. In my education, I might of called it Symmetry, in the very beginning, and science has something to say about that. While I have a real study in reductionism, the work that has been going on, I believe eventually it will lead to an understanding within science, but it has to be developed, and in my view Moody's philosophical standpoint, is where we will start.

***

So I finished the rest of the video last night. There were somethings that were quite memorable to me that stood out.I wanted to quickly move to the end of the debate where each had an opportunity as they did in the beginning to give their last assessment as to why Death is Final, or not.

I was more focused on Sean's response and reiteration of respect for people and their beliefs. This was important to me. When Moody spoke of the work that he had been doing for the last forty years with regard to NDEs and the listening to people about these experiences, these were genuine stories of,  "Death was not Final"  for Moody. I was encouraged by the votes last night, not for which side supposedly won, but by the uncertainty(final 12%) as to the question of what remains as a definitive, as to Death is Final. These shows to me that people in the end still do not know, and that,  they could not be decisive. This to me,  leaves room for work to be done.

I also liked Sean Carroll's response too,  the responsibility of acceptance as to how one may look at life given the perspective of responsibility he has having accepted his position on Death is Final. Of course he might used,  when he was a child, as one might use as Moody did, as was his thrust to understand astronomy.

I believe this to be sincere, and such a question about death that would come to all in the child's mind, a determiner of what the future would bring for him as he sat on that panel. Not so much as a Skeptic full blooded, so as to be glib with the response of,  as if Steve Novella was the amazing Randi and waited for the bet that has not been collected. :) But to remain open, as the undecided results spoke toward, as if,  more information would be needed to make a final definitive statement.

So anyway, another moment stood out in regard to Sean Carroll's response to a woman about where the energy goes once we die. His analogy of a flame going out was like the hammer statement used above, as used in the repertoire of such a question about energy and death. What I liked about the response, was as to where it put the woman in mind. If you have ever come to the point of a logical constructive immobilizing one's position, as it was on the face this woman wore,  as to where the woman could go next. That final deductive state is an important one to me.

I have much more to say about reductionism and how that research is important to me as if the table would be permanent as the atom that make it up, would be a table ad infinitive. So as sure as, matter in all it's constitutions have been described, as to say I am pointing right a it?:) We are not objects like the table. The analogy of the narrative is always important as it is spoken, and as subjective and alone as it might seem there is the greater picture of the story of the NDEr.

I must say too, that the idea of reductionism as much as materialism, causes flinches in those who speak about spiritual things, would make one from that side speak about what is not reducible?  Since energy is an important topic and how we use configuration space to surmise  it's existence,  it becomes a classification of matter. I would assume there is much still to be ascertained.  I read the blogs of other scientists who are at the front with questions phenomenologically expressed that want to see where the science goes next. Just as we have been taken t the limits of where the identification of the Higg's operates and what that energy range is.


Tuesday, February 19, 2013

Nightlights from Coast of Eastern US

ISS030-E-078095 (6 Feb. 2012) --- One of the Expedition 30 crew members aboard the International Space Station took this nighttime photograph of much of the eastern (Atlantic) coast of the United States. Large metropolitan areas and other easily recognizable sites from the Virginia/Maryland/Washington, D.C. area spanning almost to Rhode Island are visible in the scene. Boston is just out of frame at right. Long Island and the Greater Metropolitan area of New York City are visible in the lower right quadrant. Large cities in Pennsylvania (Philadelphia and Pittsburgh) are near center. Parts of two Russian vehicles parked at the orbital outpost are seen in left foreground.

Saturday, November 10, 2012

Artemis

Illustration of Artemis-P1 liberations orbits. Credit: NASA/Goddard

ARTEMIS-P1 is the first spacecraft to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. There are five Lagrangian points associated with the Earth-Moon system. The two points nearest the moon are of great interest for lunar exploration. These points are called L1 (located between the Earth and Moon) and L2 (located on the far side of the Moon from Earth), each about 61,300 km (38,100 miles) above the lunar surface. It takes about 14 to 15 days to complete one revolution about either the L1 or L2 point. These distinctive kidney-shaped orbits are dynamically unstable and require weekly monitoring from ground personnel. Orbit corrections to maintain stability are regularly performed using onboard thrusters.



Saturday, October 13, 2012

When You Look at the Cosmos......?


Scientists have turned up rare evidence that space-time is smooth as Einstein predicted, while pushing closer to a complete theory of gravity. From NASA Goddard Space Flight Center, Fermi Gamma Ray Space Telescope. See: SpaceRip.com




.....you might be enamored with how you might see the cosmos as I am.

The question of continuity of expression as some mathematical construct with out seeing the uniqueness of  lets say lensing....how might we associate with such dynamics of that continuity?

According to Einstein's theory of general relativity, the sun's gravity causes starlight to bend, shifting the apparent position of stars in the sky.


It's the way in which the Lagrangian expressions are understood or how satellite travel helps to denote the pathways throughout our universe. Are traverse pathways being suggested as we might see the holes in the cosmos as unique just to satellite travel alone? Ask yourself how the photon is influenced then? What pathways are traveled that we may see the evidence on the screen that such association measure in the spectrum are revealing of events across space and time.

Astronomers use the light-bending properties of gravity to view very distant galaxies--such as the arc shapes in this image--in a technique called "gravitational lensing.





This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel.




See Also:

Tuesday, June 26, 2012

Core Optics

A pair of polished Advanced LIGO end mirrors (ETM's)
Core optics are the 40-kg masses that form the heart of a LIGO detector. A core optic is manufactured from fused silica, polished to a few nanometers of smoothness and coated with dozens of layers of optical coatings. The result is a tuning of the balance of reflection and transmission of the mirror at the parts per million level. See: Advanced LIGO

Tuesday, March 06, 2012

Geodesy and geophysics


Mean Gravity Field



Anomalies by definition would require that we understand something about our selves that we did not know before, in that the whole history of you, is a large synopsis of everything that thinks and breath? Imagine indeed that such a vast resource could defined you as in some book to know that what would come next would be the unfolding of what you have been to what you shall become.

So I veered away from this act of who you are, toward a question of our relationship with understanding the world around us. What can exist in nature as some anomaly is really our inability to describe something in nature that awes us and had never gone deeper then then on the surface observance of who we are and where we live.


Map of free-air gravity anomalies around Britain and Ireland
Variations in the strength of gravity occur from place to place according to the density distribution of the rocks beneath the surface. Such gravity anomalies have been mapped across the British Isles and the surrounding seas and they reveal aspects of these islands’ geological structure.

(Bouguer) gravity anomaly map of the state of New Jersey (USGS)
 The Bouguer anomalies usually are negative in the mountains because of isostasy: the rock density of their roots is lower, compared with the surrounding earth's mantle. Typical anomalies in the Central Alps are −150 milligals (−1.5 mm/s²). Rather local anomalies are used in applied geophysics: if they are positive, this may indicate metallic ores. At scales between entire mountain ranges and ore bodies, Bouguer anomalies may indicate rock types. For example, the northeast-southwest trending high across central New Jersey (see figure) represents a graben of Triassic age largely filled with dense basalts. Salt domes are typically expressed in gravity maps as lows, because salt has a low density compared to the rocks the dome intrudes. Anomalies can help to distinguish sedimentary basins whose fill differs in density from that of the surrounding region - see Gravity Anomalies of Britain and Ireland for example.

Bouguer Anomaly Map of Belgium and Surrounding areas

The anomalies are calculated using a uniform Bouguer reduction density of 2.67 gr/cm3 the grid was obtained by Krigging, cell size : 5 km, search radius : 30 km. The French data are copyrighted by BRGM (France).

While the examples above help to shed light on how we can perceive earth in a way that we are not accustomed too, this idea of gravity is important to understand the way in which gravitationally we my look at the world/earth. In our early years abstractly the idea of curvature was something that did not make sense until one moved beyond the Euclidean lines of understanding to a Non Euclidean view?

To that point we did not understand what the earth look like in its pearl form in space without having left the confines of earth?

I want you too look at space as well to understand what may be conceivable even though we may talk about an anomaly in nature that to this point we did not necessarily understand until we were presented with the examples as to confront and require an explanation. So you have the earth and space to contend with here.

LTool


So we graduate with the understanding with how we have seen the earth in observatory implicitness to have it detailed in a more "ugly definition of its composed parts?" To me it's not really that ugly at all,  although as you venture to take in the color representation of the component parts of our earth's geological structure,  you learn to understand the concreteness of our definitions.

Sunday, January 24, 2010

Interplanetary Transport Network




This stylized depiction of the ITN is designed to show its (often convoluted) path through the solar system. The green ribbon represents one path from among the many that are mathematically possible along the surface of the darker green bounding tube. Locations where the ribbon changes direction abruptly represent trajectory changes at Lagrange points, while constricted areas represent locations where objects linger in temporary orbit around a point before continuing on




This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel.

Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions.

Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.


See:Interplanetary Superhighway Makes Space Travel Simpler
July 17 2002

Sunday, March 01, 2009

Gravity Wave Spectrum

PURPOSE: To show the two-dimensional standing waves on the surface of a square or circular plate.


Early perception of sound as analogy to the ideas of the WMAP background were forming in my mind when Wayne HU was demonstrating the image of polarizations in B mode. To me its as if one puts on a pair of glasses and based on an assumption of the gravitational waves, then one tends to see "all of it" in this Lagrangian way.



With the discovery of sound waves in the CMB, we have entered a new era of precision cosmology in which we can begin to talk with certainty about the origin of structure and the content of matter and energy in the universe.Polarization


This was the basis of how I was seeing the progression of Webber's experiments in using the aluminum bars in gravitational wave detection. It was also more then this that I came to the conclusion I did.

***


Sounding out the Big BangJun 1, 2007 by Craig J Hogan is in the departments of physics and astronomy at the University of Washington, Seattle, US.

Our view of the universe is about to change forever. Since science began, all our knowledge of what lies above, below and around us has come from long-familiar forms of energy: light, produced by distant astrophysical objects; and matter, in the form of particles such as cosmic rays. But we are now in a position to study the universe using an entirely different form of energy that until now has never been directly detected – gravitational waves.





Gravitational waves open up a new window on the universe that will allow us to probe events for which no electromagnetic signature exists. In the next few years, the ground-based interferometers GEO-600, LIGO, VIRGO and TAMA should be able to detect the high-frequency gravitational waves produced by extreme astrophysical objects, providing the first direct detection of these disturbances in space–time. With its much longer arm lengths, the space-based interferometer LISA will, if launched, be able to detect lower-frequency gravitational waves, possibly those generated by phase transitions in the early universe. At even lower frequencies, other experiments will look for tiny signatures of gravitational waves in the cosmic microwave background. Source: NASA.


The flow of energy in a cosmic phase transition is similar to that in a waterfall, with turbulence in the cosmic fluid generating a gravitational-wave background today.

***


Sound and fluidized interpretation seemed very close to me of the way in which such analogy would help us to look at the universe and the spaces in between cosmological locations, as if, in a three body problem relation.

The Origin of the Universe as Revealed Through the Polarization of the Cosmic Microwave Background submitted by Scott Dodelson Sun, 22 Feb 2009 14:27:37 GMT

Modern cosmology has sharpened questions posed for millennia about the origin of our cosmic habitat. The age-old questions have been transformed into two pressing issues primed for attack in the coming decade: How did the Universe begin? and What physical laws govern the Universe at the highest energies? The clearest window onto these questions is the pattern of polarization in the Cosmic Microwave Background (CMB), which is uniquely sensitive to primordial gravity waves. A detection of the special pattern produced by gravity waves would be not only an unprecedented discovery, but also a direct probe of physics at the earliest observable instants of our Universe. Experiments which map CMB polarization over the coming decade will lead us on our first steps towards answering these age-old questions.


***


See:
  • Sound Waves in the CMB
  • The Sound of the Landscape
  • Distinctions of Holographical Sound
  • B Field Manifestations
  • Friday, October 03, 2008

    Centroids

    Conclusion:The state of mind of the observer plays a crucial role in the perception of time.Einstein


    It is often I consider the Center of Gravity(Mass) as an illustration of the perspective that exists "around and within us" as a product of the natural world. We are limited by our own knowledge, yet when given, and lead to observation of what is natural in our world, we see where we had not seen before.

    \bar z = \frac{\int z dm}{m}The center of gravity (or mass), abbreviated as COM, of any object is that point within the object upon which gravity (or any body force) acts, regardless of the orientation of the object. The COM of an object may be calculated by using the principle of equilibrium.


    First off you must know that I work according to a set of principles that were discovered after a time through "subjective reflection" on the nature of mind and how it works. Of course I am no expert here, but the principles themself are realizable as an active function in the recognition of how one might interpret the world.

    \bar y = \frac{\int y \rho dV}{\int \rho dV}In the event that the density ρ of an object is not uniform throughout, the calculation of COM may be done by a similar set of equations involving the addition of density to the analysis.


    It is by taking one to recognisance of the title of this blog entry that I wanted to discuss the "subjective part" and the understanding of the "mathematical construct" that one, in my opinion exists. Just as we progress to understand the natural world around us, I believe these are synonymous with each other.

    \bar Y = \frac{\sum m \bar y}{\sum m}If a body is made up of multiple sections, each of which has a unique mass, the method for evaluating the centroid of that body is to evaluate the composite body by finite element analysis of each of the sections through the use of moment balancing, as above.



    Liminocentric structures




    You can find much on this site in regards to this issue, and I now relate centroid for consideration in the case of this topic. I presented it at the Backreaction site today to show an advancement in the thinking as we move to incorporate the knowledge. As we come to understand the natural world around us.

    Giving earth a new understanding in terms of its densities and it's relation to the gravitational contribution, it has in our new views of the globe, helped me learn and understand the feature of gravity as it extends to the cosmos.

    I have taken it a step further as many of you know to include the emotive states as valued physiological relations to what manifests in the immediate environs of the body home. While this is a far cry from the understanding of gravitational research it was inevitable for me to see an extension of how one can topological relate to the world, in this inductive/deductive mode to reason.

    While living on this earth, we always come home for reflection, and if any have not taken stock of what has accumulated during the day, then it is inevitable that is will come to reside very close to home as one sleeps through the nocturnality night. This research of subjectivity and mind had to entail "all of our activities." It had to include an understanding of the "mathematical constructs" that we observe, in order to relate to nature.

    List of Centroids




































































































    ShapeFigure\bar x\bar yArea
    Triangular areaImage:Triangle_centroid_2.svg\frac{b}{3}\frac{h}{3}\frac{bh}{2}
    Quarter-circular areaImage:Quarter_circle_centroid.svg\frac{4r}{3\pi}\frac{4r}{3\pi}\frac{\pi r^2}{4}
    Semicircular areaImage:Semicircle_centroid.svg\,\!0\frac{4r}{3\pi}\frac{\pi r^2}{2}
    Quarter-elliptical areaImage:Elliptical_quarter.svg\frac{4a}{3\pi}\frac{4b}{3\pi}\frac{\pi a b}{4}
    Semielliptical areaThe area inside the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 and above the \,\!x axis\,\!0\frac{4b}{3\pi}\frac{\pi a b}{2}
    Semiparabolic areaThe area between the curve y = \frac{h}{b^2} x^2 and the \,\!y axis, from \,\!x = 0 to \,\!x = b\frac{3b}{8}\frac{3h}{5}\frac{2bh}{3}
    Parabolic areaThe area between the curve \,\!y = \frac{h}{b^2} x^2 and the line \,\!y = h\,\!0\frac{3h}{5}\frac{4bh}{3}
    Parabolic spandrelThe area between the curve \,\!y = \frac{h}{b^2} x^2 and the \,\!x axis, from \,\!x = 0 to \,\!x = b\frac{3b}{4}\frac{3h}{10}\frac{bh}{3}
    General spandrelThe area between the curve y = \frac{h}{b^n} x^n and the \,\!x axis, from \,\!x = 0 to \,\!x = b\frac{n + 1}{n + 2} b\frac{n + 1}{4n + 2} h\frac{bh}{n + 1}
    Circular sectorThe area between the curve (in polar coordinates) \,\!r = \rho and the pole, from \,\!\theta = -\alpha to \,\!\theta = \alpha\frac{2\rho\sin(\alpha)}{3\alpha}\,\!0\,\!\alpha \rho^2
    Quarter-circular arcThe points on the circle \,\!x^2 + y^2 = r^2 and in the first quadrant\frac{2r}{\pi}\frac{2r}{\pi}\frac{\pi r}{2}
    Semicircular arcThe points on the circle \,\!x^2 + y^2 = r^2 and above the \,\!x axis\,\!0\frac{2r}{\pi}\,\!\pi r
    Arc of circleThe points on the curve (in polar coordinates) \,\!r = \rho, from \,\!\theta = -\alpha to \,\!\theta = \alpha\frac{\rho\sin(\alpha)}{\alpha}\,\!0\,\!2\alpha \rho


    Why are Planets Round?

    It is always interesting to see water in space.

    Image: NASA/JPL-
    Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

    With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.


    See:Isostatic Adjustment is Why Planets are Round?