# Dynamics and Stability – Exercises Module 3: Lagrange Equations

Course week(s) 3. Lagrange Equations

Corresponding to each module, as described in the lectures section, the teachers handed out one or more sample problems. These are worked out examples that illustrate how to work with a certain method.

Next to the given sample problems, several recommended exercises are given. These exercises can be found in the textbook of this course (Analytical Mechanics, by Josef S. Tőrők). More on this textbook can be found in the readings section.

## Recommended exercises:

Solve the exercises in the provided order:

• 2.53 (Neglect the small mass m and notice that all forces are conservative)
• 2.90
• 2.60 (The spring is unstretched when y=0)
• 2.71 (a) and (b) only
• 2.86 (Notice that there is one dot too many within the first brackets)
• 2.87
• Extra: Consider a particle with mass m moving in the xy-plane under the action of gravity -gj. The particle is subject to the constraint x sina + y cosa = C, where C and a are constants. Find the accelerations of the particle in x and y direction and the magnitude of the reaction force provided by the constraint, making use of Lagrange multipliers.
• 2.59 (Good theoretical question. Coefficients a are the partial derivatives of constraints f, which depend on the generalised coordinates only)