Section outline

    • Towards Lagrange equations... File

      Proof of the formula for the kinetic energy for a system of points in terms of Lagrangian coordinates. The matrix of the kinetic energy is symmetric and positive definite (with proof). Various examples: kinetic energy for a point in polar and spherical coordinates, the pendulum, the double pendulum and other constrained systems. Lagrangian components of forces (definition), the conservative case. Lagrange equations in the general and in the conservative case (formula and discussion, the detailed proof will be done the next Monday).  Video of Lecture 17:

      https://unipd.zoom.us/rec/share/NrKm2WrV0xuFnObFiUt8yCAoYD-da7pspIme6BHpuzFMxBCUZkrjbEWYAK851Wob.8HErXFZTkSMRcpVM 

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      Joseph-Louis Lagrange - Mécanique analytique (1788) - page 39