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Last updated:

October 4, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course reviews momentum and energy principles, and then covers the following topics

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 Curriculum

  • Course Overview 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 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 Unlimited
  • Examples for Session 16 Topics Unlimited
  • Examples for Session 17 Topics Unlimited
  • Lagrange Multipliers, Determining Holonomic Constraint Forces 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

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Massachusetts Institute of Technology
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