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Constant of motion in velocity dependent motion

  1. Jun 19, 2011 #1
    I have little confusion, we know that if Lagrangian is from from variable [itex]\theta[/itex] then conjugate momenta [itex]P_{\theta}[/itex] is a constant of motion. When it comes to velocity dependent potential like [itex]L=1/2mv^2+qv\times B[/itex] how will this differ ?
  2. jcsd
  3. Jun 20, 2011 #2


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    This cannot be right since you ad a scalar and a vector. The correct Lagrangian for the nonrelativistic motion of a point particle in an external electromagnetic field is given by

    [tex]L=\frac{m}{2} \vec{v}^2-q \Phi(\vec{x})+q \frac{\vec{v}}{c} \cdot \vec{A}(\vec{x}).[/tex]

    where [itex]\Phi[/itex] is the scalar potential, and [itex]\vec{A}[/itex] is the vector potential of the electromagnetic field. I've used Gaussian (or Heaviside-Lorentz) units.
  4. Jun 20, 2011 #3
    You are right, thanks. I actually resolved what I was asking.
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