ABSTRACT
Many real-world problems can be modelled by differential equations containing more than one dependent variable to be considered. Mathematical and computer simulations of such problems can give rise to systems of ordinary differential equations. The inverse statement is not necessarily true. For this reason, most computer programs are written to approximate the solutions for a first order system of ordinary differential equations. Differential equations might not be so important if their solutions never appeared in physical models. The electric circuit model and mechanical spring-mass model are two classical examples of modelling phenomena using a system of differential equations that almost every differential equation textbook presents. Many interesting models originate from classical mechanical problems. The most general way to derive the corresponding systems of differential equations describing these models is the Euler-Lagrange equations. Some quantities may be completely identified by a magnitude and a direction, as, for example, force, velocity, momentum, and acceleration.
