Canadian Journal of Mathematics · 1950 · 2.1K citations · 2 references
Natural SciencesMathematicsPhysicsDifferential EquationsMathematical PhysicsTheoretical PhysicsHamiltonian DynamicsHamiltonian MechanicsHamiltonian SystemsLagrangian DynamicsLagrangian MechanicsVariational FormulationConsistencyDynamic Equations Of MotionGeneralized MomentaHamilton's PrincipleHamilton-jacobi TheoryHamiltonian FormulationLagrangian FormulationSimplification
Lagrange and Hamilton each formulated dynamics in a general form, one using generalized coordinates and velocities and the other using coordinates and momenta. The study compares the relative merits of the two formulations. The paper begins with an introduction.
1. Introduction. The equations of dynamics were put into a general form by Lagrange, who expressed them in terms of a set of generalized coordinates and velocities. An alternative general form was later given by Hamilton, in terms of coordinates and momenta. Let us consider the relative merits of the two forms.
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Forms of Relativistic Dynamics
P. A. M. Dirac · Reviews of Modern Physics · 1949 · 2.1K citations · Full text