Micro Dynamics Training

Micro Dynamics Online Training_0

Mathematical Methods in Dynamics

Electromechanical Systems

Dynamics Core

Fundamental Principals of Dynamics

  • Newton’s Laws
  • Variation Principles

Methods of Formulating Equations of Motion

  • Newton’s Second Law
  • Work: Energy Principle
  • Impulse Momentum Principle
  • Angular Momentum Principle
  • D’Alembert’s Principle
  • Principle of Virtual Work
  • Hamilton’s Principle
  • Lagrange’s Equations
  • Hamilton’s Equations
  • Kane’s Equations


  • Differentiation of Vectors in Rotating Frames
  • Angular Velocity
  • Partial Velocities; Partial Angular Velocities
  • Euler Angles; Euler Parameters
  • Kinematics of Free and Interconnected Bodies

Mathematical Methods in Dynamics

  • Geometric Theory of 2nd Order Dynamical Systems; Ph~ Plane. Singular Points., Limit Cycles
  • Definition and Interpretation of Liapunov’s stability, Orbital Stability, Asymptotic Stability
  • Linearization
  • Stability Analysis of Linear Variation Equations with Constant and Periodic Coefficients; Forms of Solutions, Parametric Excitation, Floquet Theory, Infinite Determinants
  • Liapunov’s Direct Method, Complete Damping, the Hamiltonian as a Liapunov’s Function, Cyclic Coordinates, Integrals of the Motion
  • Perturbation Methods; Lindstedt’s Method, Averaging, Multiple Time Scalars; Single and Multi Degree of Freedom Systems; Jump Phenomenon, Sub harmonic Oscillations, Nonlinear Resonance

Electromechanical Systems

  • Electro mechanics; Electrostatics, Magneto statics, Induction, Maxwell’s Equations, Dielectrics, Ferromagnetism, Electromagnetic Energy, Electromechanical Transduction
  • Electric Machines: Permanent Magnetic DC Motor, Variable Reluctance and Permanent Magnetic Stepper Motors, Electrostatic Motors, Piezoelectric and Magnetostrictive Motors
  • Control/Electro mechanics Interaction: Energy Storage and Dissipation, Stability of Collocated and Non-Collocated Systems, Effects of Sensor/Actuator Dynamics, Pole/Zero Pairing, Minimum Phase/Non-Minimum Phase Systems
  • Residual Vibration: Point-to-Point Control, Minimum Time, Minimum Energy, Minimum Jerk, Frequency Shaping
  • active Piezoelectric Damping: Piezoelectricity, Piezopolymer Laminar, Distributed Sensing/Control, Modal Sensor/Actuator

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