LAGRANGIAN OPTIMIZATIONS

Author

Horia Orasanu

Abstracts

. Course unit content: This course covers Lagrangian and Hamiltonian Mechanics. Topics include main principles of Newton mechanics and , Kepler Problem, Scattering Theory, motion of many body systems, variations, d’Alembert’s and Hamilton’s Principles, generalized coordinates, Lagrange’s Equation, Conservation laws associated with spatial and time properties, theory of linear oscillations, normal modes, solid body dynamics, Hamiltonian Equation, Poisson Brackets and canonical transformations

1. Introduction.

Generally, there are two procedures used for solving variational problems that have constraints. These are the methods of direct substitution and Lagrange multipliers. In the method of direct substitution, the constraint equation is substituted into the integrand; and the problem is converted into an unconstrained problem as was done in Chapter II. In the method of Lagrange multipliers, the Lagrangian function is formed; and the unconstrained problem is solved using the appropriate forms of the Euler or Euler-Poisson equation. However, in some cases the Lagrange multiplier is a function of the independent variables and is not a constant

LAGRANGIAn OPTIMIZATIONS

Author

Horia Orasanu

a

Abstracts

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