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Possible new reformulation of classical mechanics

  1. Jul 19, 2010 #1
    Let's say someone wanted to describe the motion of a 3D object in 3D space, for example maybe a ball in real space. Instead treating the ball as a 3D entity as a whole, how about just taking any point on the ball 1d point and just describe it's motion. In my example I'm assuming the point I chosen on the 3D sphere moves with it. This would simplify the problem from a 3D problem in 3D space into a 1D problem in 3D space. I would like to make a new kind of basic reformulation of classical mechanics similar to what Lagrange did in which 3D object can be expressed as 1D points for continuous bodies. Would this idea be original or was it came up with already .
     
  2. jcsd
  3. Jul 19, 2010 #2
    I'm not a master of physics but I think that what you are talking doesn't make any sense. Sorry if I'm wrong.
     
  4. Jul 19, 2010 #3
    What if your ball is rolling as well as translating?
     
  5. Jul 19, 2010 #4

    dlgoff

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    You mean something like this?
    http://hyperphysics.phy-astr.gsu.edu/HBASE/mechanics/n2ext.html" [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Jul 19, 2010 #5
    yes something like that except the point can be any point on the object, not just the center of mass
     
    Last edited by a moderator: May 4, 2017
  7. Jul 20, 2010 #6
    Sounds like what you are suggesting is something similar to Ptolemy's theory of the movement of the planets applied to Newtonian dynamics.

    Yes, you could do that. Same as you could decimalise the octave - (someone suggested that once.)
     
  8. Jul 20, 2010 #7
    You make the problem harder not easier. Especially if the distances between the points are fixed, you deal with a rigid body that can be described by twelve variables or so, no matter how many particles it contains. That is the whole point of the 3D treatment. For 100 particles you would have to keep track of 300 variables not just 12.

    If the particles can change distances, then you are dealing with elastic bodies. These are described by continuum mechanics, which could be seen as cutting the body into an infinite number of points. But this method arrives at a global description of tensor fields in the end, because tracking a giant number of particles is much harder then dealing with a few fields in 3D.
     
  9. Jul 20, 2010 #8

    fluidistic

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    I don't think it's possible. Unless what follows is wrong, there might be at least one big problem. You have a ball which rotates and choose to consider it as a point, say a point on its surface. There's a 3 dimensional wall not that far from the ball. You also consider the wall as a point, say not on its surface to complicate things. So your system consists of 2 separated points. How can you tell when the ball and the wall are in contact? If they are in contact and are both rigid bodies then it's impossible for the points to "touch each other", there will always be a distance between them and that distance would be totally unknown unless you explain us how you calculate it, starting from the fact that you have "2 points representing" 2 different rigid bodies that are in motion and nothing else.
     
  10. Jul 22, 2010 #9
    Reducing a 3 dimensional problem in 3 space to a 1 dimensional problem in 3 space could not give a full description of the system (you would lose degrees of freedom in the process). However, this method is still interesting, but only as long as you know enough about the system to know whether or not the approximation is useful. Thermodynamics is basically what you're suggesting: describing lots of degrees of freedom in terms of macroscopic "one dimensional" parameters (If I understand what you're saying). With your single point on the rotating body, you may be able to uniquely specify one "type" of rotation. However, you would never know if there was any rotation along the axis passing through the point you select, and so in order to analyze the motion you would need to analyze all possible motions that your approximation allows for, and throw in a few parameters describing the state of "random" distributions of possible "spins" of your particle.
     
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