Ordinary Differential Equations

One-dimensional oscillations are described by linear ordinary differential equations with closed form solutions extendable to forced oscillations. Besides the Lagrangian the Hamiltonian form of mechanics is introduced. Further applications are the motion of space frames (from Chapter 3) and two species models from population dynamics. By means of qualitative analysis (using phase portraits) the long time behavior can be analyzed. The principle of linearized stability reduces the stability question to linear systems, where it can be completely studied. Finally also variational problems and optimal control problems are discussed.