1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determine a formula for (RE: vector valued functions)

  1. Apr 22, 2008 #1
    Let r(t) be a v.v.f -with the first and second derivatives r' and r''. Determine formula for
    d/dt [r.(r' x r'')] -in terms of r:

    How do we approach this one?

    maybe:
    d/dt [r.(r' x r'')] = d/dt [r.r' x r.r''] = ((r'.r' + r.r'') x r'.r'') + (r.r' x (r'.r'' + r.r''')) ??
    ...and then what?

    Is anyone able to give me a starting point -- or starting direction? -- thanks heaps
     
  2. jcsd
  3. Apr 22, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What you have now doesn't make sense. r.r' is a number, not a vector. Same thing for r.r". You can't take the cross product. You seem to be assuming that u.(v x w)= (u.v)x(u.w) and, as I just said, that product doesn't make sense.

    How about jusst using the product rule:
    d/dt[r.(r' x r")]= r'.(r'x r")+ r.(r'+ r")'. The first term is easy: (r' x r") is perpendicular to both r' and r" so its dot product with r' is ???

    Now expand (r' x r")' in the same way. Again, the first part of the sum is trivial.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Determine a formula for (RE: vector valued functions)
Loading...