A state of a molecule may described by a number of parameters, e.g., bond lengths and the angles). These bonds lengths and bond angles constitute a set of coordinates which describe the molecule. We a...A state of a molecule may described by a number of parameters, e.g., bond lengths and the angles). These bonds lengths and bond angles constitute a set of coordinates which describe the molecule. We are not going to think about any particular sort of coordinate system or set of coordinates. Rather, we are going to think about generalized coordinates, which may be lengths or angles or various combinations of them.
In deriving Euler’s equations, I find it convenient to make use of Lagrange’s equations of motion. This will cause no difficulty to anyone who is already familiar with Lagrangian mechanics. The geomet...In deriving Euler’s equations, I find it convenient to make use of Lagrange’s equations of motion. This will cause no difficulty to anyone who is already familiar with Lagrangian mechanics. The geometrical description of a mechanical system at some instant of time can be given by specifying a number of coordinates, e.g., if the system consists of just a single particle, you could specify its rectangular coordinates xyz or its cylindrical coordinates ρϕz , or its spherical coordinates rθϕ .
