- #1
stdtoast
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I have equations of motion for a projectile with air resistance: where q = [x; y]
m \ddot{q_1} = -k \dot{q_1}
m \ddot{q_2} = -k \dot{q_2} - mg
I need to convert it into state space form, with the state X = [q; \dot{q}]. I'm told state-space form is a first order vector ODE: \dot{X} = [\dot{q}; \ddot{q}] = f(X)
Now I'm confused. I can write my equations of motions in matrix form like: m\ddot{q} = -k \dot{q} - [0; mg]. Is writing this in state-space form like vectorizing it again? Also, is f(X) a matrix? It's hard for me to figure out the problem without understanding the notation...
m \ddot{q_1} = -k \dot{q_1}
m \ddot{q_2} = -k \dot{q_2} - mg
I need to convert it into state space form, with the state X = [q; \dot{q}]. I'm told state-space form is a first order vector ODE: \dot{X} = [\dot{q}; \ddot{q}] = f(X)
Now I'm confused. I can write my equations of motions in matrix form like: m\ddot{q} = -k \dot{q} - [0; mg]. Is writing this in state-space form like vectorizing it again? Also, is f(X) a matrix? It's hard for me to figure out the problem without understanding the notation...
