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Differential equations to state space form

Hi everyone,

I'm writing to ask a question about a particular physical system.

After analyzing it, I have these differential equations (the simbol ' is for the derivative):

n*h'' = F*r - k1*h' - k2*h

n*x'' + (k3-k4)*x + m*k5*g = (n/r)*h'' - r*k4*h

Now I must put them into state space form. The first equation is quite simple, but I can't solve the second one, as there is a second derivative on the input (h'') and the "m*k5*g" term.

How do I have to consider them? Could anyone help me how to get the solution?

Thanks a lot!

M.

Reply to
Michele
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I presume that the derivatives you are talking about are with respect to time, but that is not clear. You really need to define your terms and what they are variables of.

Moreover, my background with these equations is from the days before EEs used state variables. I presume they refer to some kind of lagrangian or hamiltonian formulation using generalized coordinates and momenta. I hate it when new notation is introduced for no good reason.

This also looks like a homework problem.

Bill

Reply to
<salmonegg

Looks like the h'' term is determined by the first equation. In a simulation diagram you'd just take that signal and feed it into the second equation as an input.

Not sure what you meant by the m*k5*g comment. Where is the derivative.

Reply to
dave y.

------------- You know h" =F*r.... from the first equation (in terms of h' and h). Then you can eliminate h" from the second equation. You will have 4 state variables h, h', x,x'

Don Kelly @shawcross.ca remove the X to answer

Reply to
Don Kelly

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