General formulation
Consider relation given a system of first order differential equation
- Mechanical systems are often expressed as
-
- - single equation of second order in \(p\)
- - system of first order in \(u=(p,v)\)
In general, we can write
- \(u'(t) = \mathcal{F}(u(t),t)\)
If \(\mathcal{F}\) is an affine function in \(u\)
- \(u'(t)=\mathrm{A}(t)\,u(t)+b(t)\)
When \(A\) is constant through time
- \(u'(t)=\mathrm{A}\,u(t)+b(t)\)