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Proof -- motion under a central force in text Symon Mechanics

  1. Aug 19, 2016 #1
    1. The derivation
    In a 3-dim space,a particle is acted by a central force(the center of the force fixed in the origin) .we now take the motion entirely in the xy-plane and write the equations of the motion in polar coordinate
    upload_2016-8-20_1-11-5.png

    how can i derive from these equation that
    T(kinetic energy)+V(potential)=E= upload_2016-8-20_1-13-44.png ?
    (sorry for my poor english)
    2. Relevant equations


    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Aug 19, 2016 #2

    ehild

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    Read http://leandros.physics.uoi.gr/cm1/book-cm/ch6.pdf, for example.
    You need to integrate both equations. The integral of the second one is conservation of angular momentum, that of the first one is conservation of energy.
     
  4. Aug 20, 2016 #3
    thanks!!
     
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