MR4005 Multi-Body Dynamics Syllabus:
MR4005 Multi-Body Dynamics Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES
1. To understand the important concepts of multi-body dynamics.
2. To familiar the various computational methods multi-body dynamics.
3. To characterize the nonlinear concepts of multi-body dynamics.
4. To recognize the need of control in nonlinear dynamics multi body interactions.
5. To interpret the nonlinear dynamics of multi body systems and its realization of control.
UNIT I INTRODUCTION TO DYNAMICS
Importance of Multibody Dynamics – Particle Mechanics – Rigid Body Mechanics – Deformable Bodies – Constrained Motion- -Kinematics – Rotation – Translation – Velocity- Acceleration Equations – Mechanics of Deformable Bodies – Floating Frame Reference Formulation – Inertia – Generalized Forces – Equation of Motions – Multi Body Systems – Sub Systems – Friction and Spring Nonlinear Model – Nonlinear Dynamic Equations Formulation
UNIT II COMPUTATIONAL METHODS FOR DYNAMIC ANALYSIS
Jacobian Matrix – Newton-Raphson Method – Nonlinear Kinematic Constrain Equation – System Mass Matrix – External and Elastic Forces – Acceleration Vector – Lagrangean Multiplier – Langrage’s Equation – Kinetic Energy – Hamilton Equation – Hamilton vector Field- Euler – Langrage Equation- Generalized Reaction Forces – State Vector and Equation Formulation.
UNIT III NONLINEAR SYSTEMS AND CONCEPTS
Linear Time Varying and Linearization – Input and Output Stability – Lyapunov Stability Analysis – Asymptotic Stability – Popov’s and Circle Criterion – Perturbed System – Chaos – Periodic Orbits- Index theory and Limit Cycle – Centre Manifold Theory- Normal Forms- Nonlinear analysis- Poincare Maps – Bifurcations – Maps – Vector Fields – Methods – Control System Design using Lyapunov’s Direct Method.
UNIT IV SYSTEM CHARACTERIZATION
Stability, Controllability, Observability – Phase Plane Analysis – Phase Portrait – Limit Cycle – Describing Function – Assumption – Limit Cycles.
UNIT V CONTROL OF NONLINEAR MECHANICAL SYSTEMS
Double Inverted Pendulum – Nonlinear Machineries – Robots – Suspension System – Aircraft.
TOTAL: 45 PERIODS
COURSE OUTCOMES:
Upon completion of this course, the students will be able to:
CO1: Apply the important concepts in multi-body dynamics.
CO2: Create mathematical model for capturing the dynamics of multi-body interactions.
CO3: Understand the nonlinear behaviour of multi-body dynamics.
CO4: Evaluate the control in nonlinear dynamics of multi body interactions.
CO5: Apply control for the nonlinear behaviour of multi body systems.
REFERENCES
1. Ahmed A. Shabana, “Dynamics of Multibody Systems”, Cambridge University Press, 2013.
2. Brian L. Stevens, Frank L. Lewis, “Aircraft Control and Simulation”, Wiley India Pvt Ltd, 2010.
3. Hasan Khalil, “Nonlinear Systems and Control”, Prentice Hall, 2002.
4. Mahmut Reyhanoglu, “Dynamics and Control of a Class of Under Actuated Mechanical Systems”, IEEE Transactions on Automatic Control, 44(9), 1999.
5. Stephen Wiggins, “Introduction to Applied Nonlinear Dynamics System and Chaos”, SpringerVerlag, 2000.
6. Wei Zhong and Helmut Rock, “Energy and Passivity Based Control of the Double Inverted Pendulum on a Cart”, IEEE, 2001.