Transformation Theory

Abstract

In building up the Lagrangian and Hamiltonian formulations considerable care was taken to make the form of all general relations the same for all co-ordinate systems. Any co-ordinate transformation represented by:

$$q{i^,} = q{i^,}(q1,q2, \ldots {q_n},t)$$

(7.1)

produces equations identical in form with the original ones involving the q _i ’s. More technically it may be stated that ‘the equations are covariant to point transformations’. It should be noted that the assumption is made that singular transformations are excluded from consideration.