MEAM 535 Advanced Dynamics

Fall 1999

Homework #1

This is a refresher on Newtonian dynamics and therefore a warm-up for most of you.

1. The transformation equations from spherical to rectangular coordinates a re
   



a) Find x_dot, y_dot, and z_dot in terms of r, r_dot, phi, phi_dot, theta, theta_dot.
("_dot" denotes derivative with respect to time.)

b) Find the components of basis unit vectors of rectangular system, i^, j^, and k^ along the basis unit vectors of the spheri cal system, e_r^, e_phi^, and e_theta^.
(hat ^ denotes a unit vector)



2. A massless string can safely sustain a tension T. Find the shortest time in which it can raise a weight W through height h, so that it starts at rest and comes to rest at the end of ascent.
   
3. Problem 1.21 in [HB] reproduced here for your convenience.
   ("HB" indicates the course textbook by Haim Baruh)