ABSTRACT
This chapter derives several dynamic equations of motion from variational principles. If the determinant of this matrix, sometimes called the Hessian, is not zero, then the variables of the new set are independent. This means that they could also be obtained as functions of the original variables. Hamilton's principle is general and it is applicable to complex mechanical systems. The chapter considers the simplest mechanical system of a mass particle, but since any complex mechanical system may be considered a collection of many mass particles. Hamilton's canonical equations are the result of the application of Legendre's transformation to the Lagrangian function. The relationship between the two functionals is not always easy to establish. The chapter also addresses the orbital motion of two celestial bodies moving under each other's gravitational influence. It is known from Newtonian mechanics that such a motion is planar.
