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Vector in orbital theory.

  1. Mar 29, 2014 #1
    Hi,

    I need help with the following equations.

    n = r/r (unit vector in r direction)


    v =d r/dt = dr/dt n + r dn/dt



    L = r X (mv) = mr^2 [n X (dn/dt)]

    how did this
    mr^2 [n X (dn/dt)]
    came about?

    I would expect some thing from
    r X (mv)
    to this
    m (v X r)
     
  2. jcsd
  3. Mar 31, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Start from ##\mathbf{L} = \mathbf{r} \times m \mathbf{v}## and substitute for ##\mathbf{r}## and ##\mathbf{v}## their values expressed in terms of ##\mathbf{\hat{n}}##.
     
  4. Apr 1, 2014 #3
    n = r/r
    r=rn

    v = r

    L = r X mv

    v =d r/dt = dr/dt n + r dn/dt
    L = m . rn X[ dr/dt n + r dn/dt ]
    = m [rn X dr/dt n + rn X r dn/dt]
    (red disappear since in same direction)

    = m [rn X rdn/dt]

    is this right?
     
  5. Apr 2, 2014 #4

    DrClaude

    User Avatar

    Staff: Mentor

    Correct. And you can take out the ##r^2## from the bracket as it is a scalar.
     
  6. Apr 2, 2014 #5
    ohh

    took me 1 year to figure that our. :)
     
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