Analytical Mech Homework Solutions 31

Analytical Mech Homework Solutions 31 - 3.24 The equation...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
3.24 The equation of motion is ( ) 3 Fx x x m x =− = ±± . For simplicity, let m=1. Then 3 x xx =− . This is equivalent to the two first order equations … x y = ± and 3 yxx ± (a) The equilibrium points are defined by ( )( ) 3 11 xx x x x −= − += 0 Thus, the points are: (-1,0), (0,0) and (+1,0). We can tell whether or not the points represent stable or unstable points of equilibrium by examining the phase space plots in the neighborhood of the equilibrium points. We’ll do this in part (c). (b) The energy can be found by integrating 3 dy y x x dx x y == ± ± or or () 3 ydy x x dx C + ∫∫ 224 C =−+ ` In other words … 24 2 242 yx x ETV C  = += + =   . The total energy C is constant. (c) The phase space trajectories are given by solutions to the above equation
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

Ask a homework question - tutors are online