TABLE OF CONTENTS In this chapter we give a summary of basic concepts of classical mechanics. The starting point is Newton s second law, which is included in 1. If kinematic constraints apply, the Lagrange formalism, dealt with in 2, is the appropriate framework to derive the equations of motion. An alternative formalism, presented in 3, stems from Hamilton and has certain advantages if the system is autonomous and the constraints are not time dependent. Then the energy of the system is conserved and orbits in phase space can be found from contour lines of the Hamiltonian. In 4 the application of this to the phase plane is shown. In 5 continuous media are briefly dealt with. They give rise to partial differential equations (PDE) instead of ODE. By an example, in which the so-called method of lines is used, we show that the numerical treatment of PDE may lead to ODE.
The study of differential equations is largely inspired by observations and descriptions of mechanical systems. Experiments on earth and observation of the solar system led to the concepts of position, velocity, acceleration, force, and the mathematical language describing their relations. A lot of knowledge about ODE has been gained within the framework of classical mechanics, but these insights are more generally applicable too. In this chapter we present some central issues of classical mechanics which have also proved their value elsewhere. The emphasis will be on the ideas behind the formalisms, rather than on the details of the derivations, which...
