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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

Kinematics

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