How can I solve the following differential equations to get the state-space equation?
my'' = -km' - gm
x1 = y \(\rightarrow\) x1' = x2
x2 = y' \(\rightarrow\) x2' = y''
x3 = m
u = m'
Eq1 x1' = x2
Eq2 x3 x2'' = - kx3' - gx3
The problem that I face with Eq2 specifically x3.x2''
I know X' = Ax + Bu and I know how I get it if it is only like this x2'' = ....
but there there is another variable times x2
Any suggestions!
my'' = -km' - gm
x1 = y \(\rightarrow\) x1' = x2
x2 = y' \(\rightarrow\) x2' = y''
x3 = m
u = m'
Eq1 x1' = x2
Eq2 x3 x2'' = - kx3' - gx3
The problem that I face with Eq2 specifically x3.x2''
I know X' = Ax + Bu and I know how I get it if it is only like this x2'' = ....
but there there is another variable times x2
Any suggestions!