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 .
