Dynamics of Physical System

Overview

Instructor: Prof. S. Banerjee, Department of Electrical Engineering, IIT Kharagpur.

This course covers lessons on newton's method and constraints, derivation of the Lagrangian equation, bond graph approach, vector field around equilibrium points, high dimensional linear systems, and dynamics of nonlinear systems.

One of the important elements of engineering practice is to be able to predict the behavior of the system that we design. For example, if we design a circuit, we should be able to predict how it will perform, how it will behave under certain circumstances. If we are designing a mechanical system, we should be able to do that. And that is generally done by forming a mathematical model of the system, applying different types of inputs and seeing its performance.

Syllabus

Lecture - 1 Introduction to System Elements.
Lecture -2 Newtons Method and Constraints.
Lecture - 3 Derivation of the Lagrangian Equation.
Lecture - 4 Using the lagrangian Equation to Obtain Differential Equations(Part-I).
Lecture - 5 Using the lagrangian Equation to Obtain Differential Equations(Part-II).
Lecture - 6 Using the lagrangian Equation to Obtain Differential Equations(Part-III).
Lecture - 7 Using the lagrangian Equation to Obtain Differential Equations(Part-IV).
Lecture - 8 Obtaining First Order Equations.
Lecture - 9 Application of the Hamiltonian Method.
Lecture - 10 Obtaining Differential Equations Using Kirchoff's Laws.
Lecture - 11 The Graph Theory Approach for Electrical Circuits(Part-I).
Lecture - 12 The Graph Theory Approach for Electrical Circuits(Part-II).
Lecture - 13 The Bond Graph Approach-I.
Lecture - 14 The Bond Graph Approach-II.
Lecture - 15 The Bond Graph Approach-III.
Lecture - 16 The Bond Graph Approach-IV.
Lecture - 17 The Bond Graph Approach-V.
Lecture - 18 The Bond Graph Approach-VI.
Lecture - 19 The Bond Graph Approach-VII.
Lecture - 20 Numerical Solution of Differential Equations.
Lecture - 21 Dynamics in the State Space.
Lecture - 22 Vector Field Around Equilibrium Points-I.
Lecture - 23 Vector Field Around Equilibrium Points-II.
Lecture - 24 Vector Field Around Equilibrium Points-III.
Lecture - 25 Vector Field Around Equilibrium Points-IV.
Lecture - 26 High Dimensional Linear Systems.
Lecture - 27 Linear Systems with External Input-I.
Lecture - 28 Linear Systems with External Input-II.
Lecture - 29 Linear Systems with External Input-III.
Lecture - 30 Dynamics of Nonlinear Systems-I.
Lecture - 31 Dynamics of Nonlinear Systems-II.
Lecture - 32 Dynamics of Nonlinear Systems-III.
Lecture - 33 Discrete-Time Dynamical Systems-I.
Lecture - 34 Discrete-Time Dynamical Systems-II.