We must assume that r has a third derivative.
.
But both . Do you see why?
So the final answer would be what?
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? I probably looking at this completely wrong -- there must be some simple vector calculus identities that make this easy or something.
Is anyone able to give me a starting point -- or starting direction? -- thanks heaps