Dynamics and Stability
This course will the student provide a background in advanced methods of dynamics and their application to relevant problems in aerospace engineering. The course is given in lecture form, and includes various elaborated example problems relevant for aerospace engineering.
Every module provides the lecture slides, one or more sample problems and several homework exercises. These recommended exercises and hints can be found together with the sample problems in the exercises section.
Course content: Principles of dynamics: Newton’s laws, motion with respect to non-inertial reference frames, fictitious forces, conservative systems, phase portraits, virtual work. Lagrangian dynamics: Generalised coordinates, constraints, generalised momenta, generalised forces, Lagrange equations of motion, Lagrangian function, conservative and dissipative systems, constraint forces, Lagrange multipliers, integrals of motion, Jacobi energy function, ignorable coordinates, steady motion. Stability: Definitions, stability of linearised systems, application to general problems and steady motion. Variational analysis: Extrema of integral functionals, Euler-Lagrange equation, essential and natural boundary conditions, Hamilton’s principle. Dynamics of rotating bodies: Kinematics, inertia tensor, Euler’s equations of motion, moment-free motion, Euler angles, gyrodynamics, steady precession.
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Based on a work at https://ocw.tudelft.nl/courses/dynamics-and-stability/.