Course Contents
- constraints, generalized coordinates - virtual displacements, principles of d’Alembert and Jourdain - Lagrange equations of second and first kind - generalized potentials, Lagrange formalism with friction - cyclic coordinates, canonical momentum - elements of variational calculus, Hamilton’s principle - Legendre transformations, Hamilton’s equations - Poisson brackets, canonical transformations - Hamilton-Jacobi-Theory - transition to wave mechanics
Literature
F. Kuypers: Klassische Mechanik, Wiley-VCH Verlag, 2016 W. Nolting: Grundkurs Theoretische Physik 2: Analytische Mechanik, Springer Verlag, 2014 W. Greiner: Klassische Mechanik II, Verlag Harri Deutsch, 2008 H. Goldstein: Classical Mechanics, Pearson Verlag, 2013 Weitere Literatur wird zu Beginn der Veranstaltung bekannt gegeben.
Preconditions
Basic Course in Analysis; Engineering Mechanics 1, 2, 3
Additional Information
After successful completion of the module the student is able to - classify the several types of constraints and describe mechanical systems by means of constraint forces - derive d’Alembert’s principle by means of the concept of virtual displacements - apply Lagrange’s equations for solving of mechanical problems - derive Hamilton’s equations by means of the Legendre transformations - apply Lagrange’s and Hamilton’s formalism for describing the kinematics and dynamics of point masses, point-mass systems and rigid bodies - derive the Hamilton-Jacobi equation by means of canonical transformations - understand the Hamilton-Jacobi theory as the basis for the construction of a theory of wave mechanics
Online Offerings
Moodle
- Lehrende: Dimitrios Makridis
- Lehrende: Ralf Müller