User:Egm6321.f11.team2.rho/HW1

=Problem 1.6 - Nonlinear 2nd-Order Term in Nonlinear 2nd-Order ODE (N2-ODE)=

Given
In the equation of motion (EOM) of wheel/magnet, (1) p.3-3,

$$\displaystyle c_3(Y^1,t)= M[1-\bar {R}u^2_{,SS}(Y^1,t)] $$

Find
Show $$\displaystyle c_3(Y^1,t)\ddot Y^1$$ is nonlinear with respect to $$\displaystyle Y^1$$

Solution
 EGM 6341 Fall 2011 (PEA1 F11) Team 2 HW1.6 (solved on my own)

Linearty has to satisfy the following condition:

Nonlinearty is the condition not satisfing the above statement.

In the given equation, the linearity of $$\displaystyle u^2_{,SS}(Y^1,t)$$ is assumed.

The results show:

Thus,

This proves that $$\displaystyle c_3(Y^1,t)\ddot Y^1$$ is nonlinear wiht respect to $$\displaystyle Y^1.$$