# 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

© 2017 School of Civil Engineering, ΕΜΠ