Topic Description

Topic Description
# Topic Description Syllabus
1 A Quick Review of Cartesian Tensors: Introduction, Summation Convention, Cartesian Tensors, Gradient, Divergence, and Curl Dyads and Dyadics
2 Introduction and Review of Undergraduate Dynamics: Introduction, Some Basic Definitions, Newtonian Laws, Kinematical Quantities, Time Derivative of a Vector
3 Kinematics: Rotation Transformations, Space-Fixed Rotation, Rotation about an Arbitrary Axis, Infinitesimal Rotations and Angular Velocity Vector
4 Path Variables
5 Orthogonal Curvilinear Coordinates
6 Euler’s Angles
7 Kinematic (Moving) Reference Frame (KRF)
8 Kinematic (Moving) Reference Frame (KRF)
9 Particle Dynamics: Introduction, Equations of Motion of a Particle
10 Newton’s Equations of Motion for a System of Particles
11 The Kinetic States (Momentum and Moment of Momentum), The Kinetic Principles, Linear and Angular Impulse, Principle of Work and Energy
12 Introduction to Gyromechanics
13 Introduction to Gyromechanics (Continue)
14 Solution of Some Problems
15 Hamilton’s Principle
16 Hamilton’s Principle: Introduction, Concepts of Calculus of Variations
17 Lagrange’s Equations of Motion for Dependent Set of Generalized Coordinates
18 Lagrange’s Equations of Motion for Independent Set of Generalized Coordinates
19 Lagrange’s Equations of Motion: Introduction, Generalized Coordinates and Degrees of Freedom
20 Virtual Work, Leibniz Equation of Motion, Conservative Force Field
21 Energy Principles: Kinetic Energy, Work
22 Kinetic Principles for System of Particles and RBs in NNRF
23 MIDTERM EXAMINATION
24 Kinetic Principles of a Particle in NNRF
25 Kinetic Principles in Non-Newtonian Reference Frame: Introduction
26 Modified Euler’s Equations, Rigid Body Rotation about an Invariant Axis
27 Generalized Form of Euler’s Equation
28 Rigid Body Dynamics: Kinetic State of a Rigid Body, Kinetic Principles of Rigid Bodies
29 Inertia Tensor for a Continuum, Transformation of Inertia Properties
30 Inertia Tensors: Inertia Tensor for a System of Particles