ABSTRACT

In the preceding material, there has been considerable emphasis placed on finding analytic formulas for solutions to differential equations. In this chapter, fundamental considerations are presented which have to do with whether a solution even exists, and in any case; how to find such solutions. Lagrangian mechanics provides many examples of situations in which these are the two questions of most importance. This is not a book on modeling or mechanics so only a very brief introduction to this is given. The reason for doing so is to show that it is common to encounter equations which cannot be solved using standard techniques.