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Dynamics of the rigid body

Course Description:

The course aims to teach students the basic topic of the subject and to develop the students analytical and problem solving abilities in the following topics : Kinematics of a particle, Kinematics of a rigid body, Kinetics of a particle and for a system of particles, Kinetics of a rigid body, Vibrations, Lagrange’s equations, Hamilton’s principle

Prerequisite Knowledge

Mechanics of Rigid Body, Differential Equations, Linear Algebra

Course Units

# Title Description Hours
1 Kinematics of particles (curvilinear motion) 3
2 Kinematics of particles (coordinate systems: Cartesian, normal-tangential systems ) 3
3 Kinematics of Rigid Bodies (translation, rotation about an axis, planar kinematics) 3
4 Kinematics of Rigid Bodies (General motion, Relative motion) 3
5 Dynamics (Kinetics) of particles (mass, force, Newton’s Law) 3
6 Dynamics (Kinetics) of particles (Work-Energy, Impulse - Momentum) 3
7 Dynamics (Kinetics) of system of particles (Newton’s Law, Work-Energy, Impulse – Momentum) 3
8 Dynamics (Kinetics) of Rigid Bodies (planar dynamics, Newton’s Law , Euler’s equations of motion 3
9 Dynamics (Kinetics) of Rigid Bodies (Work, Energy, Momentum, Moment of Momentum) 3
10 Vibrations (free vibrations of mass spring systems) 3
11 Vibrations (Force vibrations of damped systems) 3
12 Lagrange Equations , Hamilton’s Principle 3
13 Lagrange Equations , Hamilton’s Principle 3

Learning Objectives

With the successful completion of the course, the students will be able to formulate the equations of motion of a rigid body moving in 2D or 3D space using various methods of analysis. Furthermore, the course is fundamental for further studies in structural dynamics, seismic design and structural control.

Teaching Methods

Teaching methods Class presentation. Solution of example problems in the class

Student Assessment

  • Final written exam: 70%
  • Mid-term exam: 20%
  • Problems - Applications: 10%

Textbooks - Bibliography

  1. Δυναμική, Beer F., Johnston R., Eisenberg E.., 9η Έκδοση, ISBN: 978-960-418-400-2, 2012.
  2. Μηχανική του απολύτως στερεού Κινηματική και Δυναμική, Α. Γ. Μαυραγάνης, ISBN 978-960266-335-6, 2012, Συμμετρία.
  3. Εφαρμοσμένη Δυναμική, Σ. Νατσιάβας, ISBN :960-431-256-1, 1994, εκδ. Ζήττη
  4. Δυναμική Στερεού Σώματος, Γ. Παπαδόπουλος & Β. Βαδαλούκα, ISBN: 978-960-89239-7-3, 2010.

Lecture Time - Place:

  • Monday, 10:45 – 13:30,
    Rooms:
    • ΖΑμφ. Αντ. Υλ. 201
    • ΖΑμφ. Αντ. Υλ. 202