Converting a nonlinear eqn of motion to a state-space model

[Sean L]

Homework Statement

equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot.

Homework Equations

The Attempt at a Solution

Since variables q1 and q2 are coupled in the equations of motion, so I haven't been able to come up with a way to decouple them and makes a state-state equation. Any insights on this would very much be appreciated.

 

[DaveE]

What are g₁ and g₂?

 

[rude man]

Homework Statement

View attachment 238367
equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot.

Homework Equations

The Attempt at a Solution

Since variables q1 and q2 are coupled in the equations of motion, so I haven't been able to come up with a way to decouple them and makes a state-state equation. Any insights on this would very much be appreciated.

I've taken an entire semester of state space techniques and have yet to find an example of applying the technique to a non-linear problem.