Lagrange’s equations are ordinary differential equations that the path must
satisfy. They can be used to test if a proposed path is a realizable path of the
system. However, we can also use them to develop a path, starting with initial
Assume that the state of a system is given by the tuple . If we are
given a prescription for computing the acceleration , then
and we have as a consequence
and so on.
So the higher-derivative components of the local tuple are given by functions . Each of these functions depends on lower-derivative components of the local tuple. All we need to deduce the path from the state is a function that gives the next-higher derivative component of the local description from the state. We use the Lagrange equations to find this function.
— Structure and Interpretation of Classical Mechanics
The Lagrange equation:
where is a structure that can be represented by a symmetric square matrix, so we can compute its inverse.
— Me@2022-06-30 11:33:27 AM
2022.06.30 Thursday (c) All rights reserved by ACHK