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This course reviews momentum and energy principles, and then covers the following topics:
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English
English [CC]
FREE
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Description
Hamilton’s principle and Lagrange’s equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems.
This course was originally developed by Professor T. Akylas.
Course content
- Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle Unlimited
- Examples of Single Particle Dynamics Unlimited
- Examples of Single Particle Dynamics (cont.) Unlimited
- Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle Unlimited
- Dynamics of Systems of Particles (cont.): Examples Unlimited
- Translation and Rotation of Rigid Bodies Existence of Angular Velocity Vector Unlimited
- Linear Superposition of Angular Velocities Unlimited
- Linear and Angular Momentum Principle for Rigid Bodies Unlimited
- Work-energy Principle for Rigid Bodies Unlimited
- Examples for Lecture 8 Topics Unlimited
- Examples for Lecture 9 Topics Unlimited
- Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid Unlimited
- Generalized Coordinates, Constraints, Virtual Displacements Unlimited
- Generalized Coordinates, Constraints, Virtual Displacements (cont.) Unlimited
- Virtual Work, Generalized Force, Conservative Forces Unlimited
- D’Alembert’s Principle Extended Hamilton’s Principle Principle of Least Action Unlimited
- Examples for Session 16 Topics Unlimited
- Examples for Session 17 Topics Unlimited
- Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange’s Equation for Nonholonomic Systems, Examples Unlimited
- Stability of Conservative Systems Unlimited
- Linearized Equations of Motion Near Equilibria of Holonomic Systems Unlimited
- Linearized Equations of Motion for Conservative Systems Unlimited
- Example for Session 23 Topics Unlimited
- Damped and Forced Vibrations Near Equilibria Unlimited
Instructor
Massachusetts Institute of Technology
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