PHY354H1 Lecture Notes - Conservative Force, Projectile Motion, Escape Velocity
Document Summary
Lecture 21: energy phase diagrams, and en- ergy conservation in 3d: relevant text sections: morin 5. 3. The view from phase space: for a conservative one dimensional system, the energy. 2 mv2 + v (x) (1) is conserved following the motion. Notice that e is written as a function of v and x. We can imagine plotting isosurfaces of e as functions of v and x in the format of a contour plot. In this plot, the trajectories of particles will go along surfaces of constant energy. Let"s consider three examples: a spring with v = 1. 2 (2) x = (cid:112)2e/(km) are the turning points where v = 0. We might and describes an ellipse for each value of e > 0. The points have expected this behaviour, since we already determined that sinusoidal motion corresponds to ellipses in phase space.
