{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Analytical Mech Homework Solutions 31

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

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

3.24 The equation of motion is ( ) 3 F x x x mx = = ±± . For simplicity, let m=1. Then 3 x x x = ±± . This is equivalent to the two first order equations … x y = ± and 3 y x x = ± (a) The equilibrium points are defined by ( )( ) 3 1 1 x x 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 y dy x x dx C = + 2 2 4 2 2 4 y x x C = + ` In other words … 2 4 2 2 4 2 y x x E T V C = + = + = . The total energy C is constant. (c) The phase space trajectories are given by solutions to the above equation
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online