Consider a sinusoidal coordinate system (u, w). The transformation of the coordinates cartesian (...
Consider a sinusoidal coordinate system
(u, w). The transformation of the coordinates cartesian (x, y) to
parabolic coordinates are given by:
u(x,y) = x, q(x, y) = y - a sin (bx), with a and b constants.
(a) Obtaining the inverse transformation, from get the metric in
the sinusoidal system.
(b) Assumes that an observer moves with constant velocity v those
components are
v^x = v and v^y = 0. What is the speed of the observer in the
system (u,w)?
(c) Samples that the speed component v^w it is not
independent of time to weigh that the magnitude of v is constant.
Explain why v^w is not constant despite that the vector v always
points in the same direction and its magnitude is constant.
Homework Answers
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