Michel Borel was previously a lecturer in mechanics at the CNAM Center in Versailles, Associate Professor at École nationale supérieure du pétrole et des moteurs (ENSPM), and an engineer for the company Bertin and at the General Armament Direction (DGA).Georges Vénizélos is Professor and Chair of mechanical systems design at Conservatoire National des Arts et Métiers (CNAM) in France. His research field concerns vibration control. mament Direction (DGA).

• Introduction ixTable of Notations xvChapter 1. Location of Solid Bodies 11.1. The notion of system of reference 11.2. Frame of reference 21.2.1. Setting up a frame of reference 21.2.2. Various types of frames of reference 91.3. Location of a solid body 141.3.1. The principle of locating a solid 151.3.2. Location parameters of a solid 151.3.3. Coordinates of the position vector 161.3.4. Exercises 201.4. Positioning of a system of reference connected to a solid 221.4.1. Several examples of location systems of reference 221.4.2. General location parameters 261.4.3. Euler angles 281.4.4. Changes of basis in the Euler representation 291.4.5. Exercises 361.5. Vector rotation R u ,α 441.5.1. Exercises 471.6. Other exercises 511.6.1. Exercise 7 – Location of an airplane – Euler angles 511.6.2. Exercise 8 – Vector rotation 551.6.3. Exercise 9 – Vector rotation 571.6.4. Exercise 10 –Vector rotation 59Chapter 2. Solid Kinematics 632.1. Generalities on moving solids 632.1.1. Concept of a rigid material system 632.1.2. Notion of time 642.1.3. Kinematic components of a solid 652.2. Kinematics of a material point 662.2.1. Position vector 662.2.2. Trajectory of a material point in a reference frame 662.2.3. Velocity of a material point in a reference frame 672.2.4. Components of the velocity vector or velocity 682.2.5. Derivative of a vector in a basis 712.2.6. Acceleration vector of a material point in a reference frame 742.2.7. Exercises 792.3. Velocity field associated with the motion of the rigid solid 852.3.1. Fundamental formula for the velocity 852.3.2. Use of matrix notation 872.3.3. Velocity-distributing torsor 892.3.4. Partial distributing 892.4. Acceleration field of the rigid solid 912.4.1. Derivative in relation to the time of the rate of rotation 912.4.2. Derivation of a vector of the solid 922.4.3. Fundamental formula of acceleration 922.4.4. Matrix notation of the vectorial product 922.4.5. Exercises 932.5. Motion with fixed plane 1022.5.1. Position of the problem 1022.5.2. Instantaneous rotation center 1042.5.3. Fixed and mobile centroids of the motion 1062.5.4. The instantaneous center of rotation on the fixed centroid and on the movable centroid 1072.5.5. Physical interpretation of the notions of fixed centroid and mobile centroid 1082.5.6. Exercises 1092.6. Combining motions within a mobile frame of reference 1172.6.1. Position of the problem 1172.6.2. Trajectory of a material point in the different frames 1182.6.3. Combination of velocities 1182.6.4. Combination of accelerations 1232.6.5. Application exercises 1282.7. Relative motion of two rigid solids in contact 1412.7.1. Position of the problem 1412.7.2. Velocity-distributing torsors 1412.7.3. Characterization of motions 1422.7.4. Nature of the contact between (S1) and (S2) 1432.7.5. Exercises 1452.8. Other exercises 1562.8.1. Exercise 21 – Motion with fixed plane 1562.8.2. Exercise 22 – Combination of motions 1602.8.3. Exercise 23 – Kinematics of contact in a system 169Chapter 3. Kinetics of Solid Bodies 1773.1. The mass of a continuous mechanical set (D ) 1773.1.1. The notion of measure on a continuous mechanical set 1783.1.2. The volume and the mass of a continuous mechanical set 1783.2. Center of the measure of μ on (D ) 1793.2.1. Definition 1793.2.2. Uniqueness of the center of measure 1793.2.3. Center of measure of two disjoint sets 1803.2.4. Coordinates of the center of measure in a system of reference (λ) 1813.3. Interpretation of the notion of center of measure 1833.4. Kinetic torsor of a mechanical set (D ) 1833.4.1. Definition – linear momentum 1833.4.2. Kinetic torsor { } S pλ of a rigid solid body 1853.4.3. Inertia operator OS ( | ) I S m 1863.4.4. Kinetic torsor and change of basis 1963.5. Dynamic torsor of a mechanical set (D ) 1983.5.1. Definition 1983.5.2. Dynamic torsor of the rigid solid body (S) 1993.6. Kinetic energy of a mechanical set (D ) 2063.6.1. Definition 2073.6.2. Kinetic energy of the free rigid solid body (S) 2073.6.3. Derivatives of the kinetic energy - Lagrangian 2133.6.4. Exercises 2233.6.5. Kinetic energy of a constrained solid 2383.7. Partition of a continuous mechanical set (D ) 239Bibliography 241Index 243