Dynamics and Kinematics

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Title: 
Dynamics and Kinematics
Course ID: 
ΓΕ0147
Course Description: 
Semester: 
4th
Διδάσκων: 
ΕCTS: 
4.5
Compulsory
Description: 

 

COURCE

OUTLINE AND LEARNING OBJECTIVES

TUTORIAL/LABORATORY TRAINING EXERCISES

1

Kinematics of a point like body. Displacements and motion. Velocity and acceleration.   Methods for determination of a point like object motion.

Curvilinear and plane motion.

Problems and  Solving Techniques

2

Harmonic oscillation. Mathematical pendulum.

Central motion.

Problems and  Solving Techniques

3

Solid object kinematics. Rotational kinematics. Rotation of a body around a fixed axis.

Problems and  Solving Techniques

4

Rotation of a solid body around a point.

Euler angles and equations.

Planar motion of a solid object. Kinematical constrains.

Velocity projection theorem.

Absolute and relative motion. Coriolis theorem.

Problems and  Solving Techniques

5

Dynamics of a point like body. Angular momentum and acceleration definition. Work – kinetic energy theorem. Angular momentum and angular momentum theorem

Problems and  Solving Techniques

6

Conservative systems Static torque.

Energy conservation.

D’Alembert principle. Relative motion.

Problems and  Solving Techniques

7

Dynamics of a solid body. Impulse.  Center of mass. Torque of inertia. Parallel axes theorem. Inertia ellipsoid. Kinetic energy. Euler dynamical equations

Problems and  Solving Techniques

8

D’ Alembert – Lagrange principle. Possible displacements.  Motion degrees of freedom. 

Unilateral and bilateral constrains.

General equation of dynamics.

Problems and  Solving Techniques

9

Collision. General theorems of collision. Momentum and impulse. Conservation of momentum. Collisions and kinetic energy. Elastic and  inelastic collisions. Friction. Collision coefficient. Central collisions. Head-on and off-center collisions.

Problems and  Solving Techniques

10

Introduction to Analytical Dynamics. Generalized coordinates. Lagrange equations.

Problems and  Solving Techniques

11

Principle of least action. Calculus of variations. Hamilton equation.

Problems and  Solving Techniques

12

Small oscillations. Free and forced oscillation. Systems and oscillations of systems with two or more degrees of freedom. Lagrange equations.

Problems and  Solving Techniques

13

Special Relativity. Introductory concepts.

The covariant of  the laws of motion. Principle of special relativity. Lorentz transformations.

Minkowski time and space. Time dilation.

Problems and  Solving Techniques

14

Lorentz transformations.

Lagrange and Hamilton equations.

Problems and  Solving Techniques

 

Recommended Reading:

 

  • D. Panagiotounakos and G. Papadopoulos (NTUA)  “Theoretical Mechanics
  • S. Timoshenko,  “Technical Mechanics, Volume 2”,