Analytical Methods in Dynamics and Vibrations (Mech 425, Spring 2021, Lehigh U.)
Aug 09, 2021
Topics to be covered include coordinate systems, conservation laws, equilibrium and stability, systems of particles, variable-mass systems, transport equation; basic concepts from variational calculus; generalized coordinates, holonomic & nonholonomic constraints, generalized forces, D'Alembert's principle, Hamilton's principle, Lagrange's equations, generalized momenta; 3D rigid-body motion, inertia tensors, Euler angles, axis-angle representation, Hamilton's and Lagrange's equations for rigid bodies; oscillations, free and forced response of linear systems, linearization of nonlinear systems, discrete eigenvalue problem; chaotic systems, perturbation theory; additional topics: configuration spaces, forward and inverse kinematics, Jacobian, singularities, position control, nonholonomic systems.
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Lecture Topics:
- LECTURE 28 (Spinning Top Example)
- LECTURE 27 (Lagrange's Equation for Rigid Body, Spinning Top Example)
- LECTURE 26 (Work-energy Principle, Lagrange's Equations for Rigid Bodies)
- LECTURE 25 (Rigid Body Equations of Motion)
- LECTURE 24 (Moment Equation)
- LECTURE 23 (Kinetics of Rigid Bodies)
- LECTURE 22 (Motion Relative to a Rotating Frame)
- LECTURE 21 (Moment of Inertia Matrix)
- LECTURE 20 (Rigid Body Kinematics, Linear Momentum, Angular Momentum)
- LECTURE 19 (Representation of Spatial Rotations, Rigid Body Kinmatics)
- LECTURE 18 (Hamilton's equation Problem, Spatial Rotations)
- LECTURE 17 (Hamilton's Equations)
- LECTURE 16 (implementation of Lagrange's equation using Mathematica, generalized momenta, Hamiltonian mechanics)
- LECTURE 15 (Constrained Lagrange Equation for Bicycle Problem, MATLAB implementation)
- LECTURE 14 (Constrained Lagrange Euations, example problem, solution approach)
- LECTURE 13 (Constrained Euler-Lagrange Equation)
- LECTURE 12.2 (Lagrange's Equations of Motion)
- LECTURE 12.1 (Euler Lagrange Equation Review)
- LECTURE 11 (calculus of variation)
- LECTURE 10 (multi dof vibrations, phase plots, calculas of variation)
- LECTURE 9 (multi-dof vibration)
- LECTURE 8 (Forced vibration, Multi-dof vibration)
- LECTURE 7 (Forced Vibration)
- LECTURE 6 (Vibrations in 1-dof Systems)
- LECTURE 5 (Conservation Principles, Equilibrium, Variable mass systems)
- LECTURE 4 (Conservation Principles)
- LECTURE 3 (Constraints, Newton's Laws of Motion, Problem review)
- LECTURE 2 (Degrees of Freedom, Generalized Coordinates, Holonomic and non-Holonomic Systems)
- LECTURE 1 (Coordinate Systems, Coordinate Transformations, Jacobian)