GEO 103 Lecture 3: GEO 103 Lecture 3 Notes

Write down the Lagrangian for a projectile (subject to no air resistance) in terms of its Cartesian coordinates (x, y, z), with z measured vertically upward.

The motion of a very massive object is hardly affected by whatwould seem to be a substantial force. Consider a supertanker, witha mass of 2.2×10^8 kg.
If it is pushed by a rocket motor (thrust force of a rocket motoris 5.0 x10^6 N) and is subject to no other forces, what will be themagnitude of its acceleration?

Consider the motion oftwoparticles subject to a repulsive inverse-squareforce.Show that this system has no states with E < 0 (asmeasured inthe CM frame), and that in all states with E > 0, therelativemotion follows a hyperbola. [Hint: You can closely followtheanalysis of Sections 8.6 and 8.7 (in Classical Mechanics1st)except that you must reverse the sign of the force. Assumeangularmomentum does not = 0.]