- 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
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