Movement Equations 3

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.

• Introduction ixTable of Notations xiiiChapter 1 Fundamental Principle of Dynamics 11.1 The fundamental principle of dynamics and its scalar consequences 11.1.1 Fundamental principle of dynamics 11.1.2 Choosing a frame 21.1.3 Preferred time scale 51.2 Secondary principles 71.2.1 First secondary principle of the separation of effects 71.2.2 Second secondary principle of effort generators 81.2.3 Third secondary principle of effort receivers 81.3 Motion of a set (D) in a given frame〈λ〉 91.3.1 Presentation of the context 91.3.2 Combination of accelerations 101.3.3 Coriolis inertial torsor 101.3.4 Drive inertial torsor 111.3.5 Relation between the dynamic torsors in the two frames 121.3.6 Applying the fundamental principle 131.4 Motion of a non-deformable solid in a given frame 141.4.1 Coriolis inertial torsor 141.4.2 Drive inertial torsor 16Chapter 2 Solid in Space Efforts and Links: Power 192.1 Degrees of freedom of a solid 192.2 Free solid 202.2.1 Velocity distributing torsor 202.2.2 Kinetic torsor 212.2.3 Dynamic torsor 212.2.4 Kinetic energy 222.2.5 Applying the fundamental principle of dynamics 222.3 Linked solids and links 232.3.1 Links 232.3.2 Configurable links 242.3.3 Linked solids 252.4 Virtual power developed on a material set (D) 282.5 Power of the efforts exerted on a solid 302.5.1 Definition 302.5.2 Discrete force field 302.5.3 Non-deformable mechanical set 312.5.4 Continuous mechanical set 312.6 Properties of power 322.6.1 Powers developed in two distinct frames 322.6.2 Case of a system of forces equivalent to zero acting on a solid 322.6.3 Case of a system of forces equivalent to zero acting on a deformable mechanical set 332.6.4 Partial powers 34Chapter 3 Scalar Consequences and Movement Equations 353.1 Establishment principle of the movement equations 353.1.1 Vector projection 363.1.2 Torsor products 373.1.3 Choice of representative scalar consequences 383.2 Movement equations of a solid 393.2.1 Scalar consequences via vector projection 393.2.2 Scalar consequences of the analytic mechanics of motion 573.2.3 Linear independence of torsors 583.2.4 Exercise 3 – Scalar consequences using analytical mechanics 603.3 Movement equations of the free solid 723.4 Movement equations of the linked solid with configurable links 753.4.1 Velocity distributing torsor and partial distributing torsors 753.4.2 Case of configurable links independent of time 763.4.3 Case of configurable links dependent on time 773.4.4 Perfect configurable links 783.5 Energetic expression of the equations of analytical mechanics 783.5.1 Case of configurable links explicitly independent of time 783.5.2 Case of configurable links explicitly dependent on time 793.6 Summary example 813.6.1 Locating the solid 813.6.2 Links 833.6.3 Solid kinematics 833.6.4 Kinetics of the solid 85Chapter 4 Particular Applications 974.1 Simulation of the motion of Earth 974.1.1 Application of the fundamental principle 974.1.2 Theorem of dynamic moment at G 994.1.3 Theorem of dynamic resultant 1084.2 Foucault’s pendulum 1144.2.1 Observation of the phenomenon 1144.2.2 Analyzing the phenomenon 116Chapter 5 Methodological Formulary 1275.1 Reference outline on the motion of a solid 1275.1.1 Representation of a frame 1275.1.2 Reference frame 1295.1.3 Situation of the solid 1305.1.4 Notion of basis in a frame 1335.2 Kinematics of the solid 1335.2.1 Kinematics of a material point M 1345.2.2 Kinematics of non-deformable solids 1395.3 Principle of motion with fixed plane 1425.3.1 Kinematics of a solid 1425.3.2 Fixed and mobile centroids in a motion with fixed plane 1435.4 Combination of motions 1455.4.1 Combination of velocities 1455.4.2 Combination of accelerations 1475.5 Kinetics of non-deformable solids 1485.5.1 Center of measure 1485.5.2 Linear momentum and kinetic torsor 1495.5.3 Dynamic torsor 1535.5.4 Kinetic energy 155Bibliography 161Index 163