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Book Description

This volume is the focal point of the work undertaken in the previous volumes of this set of books: the statement of the fundamental principle of the dynamics whose implementation, according to two paths whose choice depends on the problem to be treated, leads to equations of motion.

In order to achieve this, it is treated first of all in the context of solids in their environment, as a prerequisite for the formulation of the fundamental principle. Then, in addition to its use in some exercises, the approach is illustrated by three particular cases.

The first is an example where it is developed end-to-end and addresses the two approaches that lead to the equations of motion. The two other examples deal with two classical but important subjects, the movement of the Earth according to the hypotheses that can be stated about it, and Foucault’s pendulum.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Introduction
  5. Table of Notations
  6. 1 Fundamental Principle of Dynamics
    1. 1.1. The fundamental principle of dynamics and its scalar consequences
    2. 1.2. Secondary principles
    3. 1.3. Motion of a set in a given frame λ
    4. 1.4. Motion of a non-deformable solid in a given frame
  7. 2 Solid in Space. Efforts and Links: Power
    1. 2.1. Degrees of freedom of a solid
    2. 2.2. Free solid
    3. 2.3. Linked solids and links
    4. 2.4. Virtual power developed on a material set
    5. 2.5. Power of the efforts exerted on a solid
    6. 2.6. Properties of power
  8. 3 Scalar Consequences and Movement Equations
    1. 3.1. Establishment principle of the movement equations
    2. 3.2. Movement equations of a solid
    3. 3.3. Movement equations of the free solid
    4. 3.4. Movement equations of the linked solid with configurable links
    5. 3.5. Energetic expression of the equations of analytical mechanics
    6. 3.6. Summary example
  9. 4 Particular Applications
    1. 4.1. Simulation of the motion of Earth
    2. 4.2. Foucault’s pendulum
  10. 5 Methodological Formulary
    1. 5.1. Reference outline on the motion of a solid
    2. 5.2. Kinematics of the solid
    3. 5.3. Principle of motion with fixed plane
    4. 5.4. Combination of motions
    5. 5.5. Kinetics of non-deformable solids
  11. Bibliography
  12. Index
  13. End User License Agreement