Week 
Subject 
Related Preparation 
1) 
Defining kinematics, geometric properties of vectors and sliding vectors 

2) 
Vector and analytic expressions of sliding vector, comoment, geometric interpretation and results. Vector coordinates of a line, detailed studies on it and related results. Introduction to tensors. 

3) 
Composition of tensors, moments, equivalence class, moment with respect to an axis, analytic expressions, invariant and axis. Special tensors and examing them. Warignon theorem, related theorems and results. 

4) 
Operations on tensors, which leave them equivalent to themselves, reduction and examining of tensors. Algebraic structure of tensors. Comoment, automoment, invariant of a system, related theorems and results. 

5) 
Line to zero moment, polar plane, conjugate lines, Plucker coordinates related theorems and problems. Vector production tensors; theorem and problems 

6) 
Definition of kinematics. Kinematics in plane. Constructing plane motion of oneparameter, translation and rotation. Derivation equations of motion and interpretations. Relative velocity. 

7) 
Angular velocity, absolute and drift velocity. Composition of velocities and interpretation. Pole of instantaneous rotation orbits of poles. The relation of plane motion with the locus of pole points. 

8) 
Rolling of pole curves without sliding. Inverse motion, examples of motion. Moving coordinate system and norming them. Pffafian forms. 

9) 
Constructing motion in moving planes. Expressions of relative, drift and absolute velocity and composition of velocities. Expressing pole points with Pffafian forms. Chain of plane moving with respect to each other. Pole of rotation, line of pole. 

10) 
Canonic relative system. Differential forms and interpretation of them. Orbit curve and its curvature. Center of curvature. Euler Savary formula. 

11) 
Point correspondence in plane motion. Examples and applications of EulerSavary formula. Introduction to sphere kinematics. Motions around a fixed pointy sphere motions. Showing motion on sphere. Introduction to sphere motions of one parameter. 

12) 
Velocities in sphere motion of one parameter (absolute, relative and drift velocities), Pffafian vector. Composition of motions, related theorems and results. Reducing sphere motion 

13) 
Canonic relative system. Pol curves and rolling of them without sliding. Theorems and results about moving spheres of same center and moving with respect to each other. 

14) 
Correspondence of Euler Savary formulas of orbit curves in sphere motion. Space kinematics (introduction to kinematics in space) 
