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mickelan mickelan
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11 years ago
If r(t) * r(t) = c, then r(t) * r'(t) = 0.

r(t) is a vector valued function, and r'(t) is its derivative. c is a constant. The * indicates dot product (not sure what else to use).

I don't need a whole proof (it would be nice though), but an idea of where to start would be very helpful. A proof in two dimensions (as opposed to three) is all I need. Thanks in advance.
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#1
11 years ago
r(t) = (x(t) ; y(t))

r(t) * r(t) = (x(t))² + (y(t))² = c
 derivating :

2x(t) x'(t) + 2y(t) y'(t) = 0

or x(t) x'(t) + y(t) y'(t) = 0

or r(t) * r'(t) = 0
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