Movement Equations 3

Dynamics and Fundamental Principle

Michel Borel, Georges Vénizélos

• Publisher: Wiley-ISTE
• Year: 2017
• ISBN:
  9781119467083
• Edition: 1
• Topic: Ciencias físicas
• Subtopic: Mecánica

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.

1
Fundamental Principle of Dynamics

The movement equations that have been presented in the previous volumes of this series on non-deformable solid mechanics are the scalar expression of the fundamental principle of dynamics and the different consequences that stem from it. But in using this principle, the choice of the frame in which to apply it (depending on the motion being studied) is crucial. The step is therefore to see how this decision can be made so that mechanics users may have a proper frame for the studied motion that is suitable for its context.

1.1. The fundamental principle of dynamics and its scalar consequences

The fundamental principle of dynamics is one of the general laws that govern mechanics just as the secondary principles that will be presented in section 1.2 later on. Their formulation is the result of experimental observations and measures; their validity is essentially based on the fact that they are universally used.

1.1.1. Fundamental principle of dynamics

There exists at least one reference frame

g

, called Galilean, and a way to measure time (called the preferred time scale), such as, at any given time and whatever the considered physical set

, the dynamic torsor

of the set motion through the frame

g

is equal to torsor

representing the ef...

Table of contents

• Cover
• Table of Contents
• Title
• Copyright
• Introduction
• Table of Notations
• 1 Fundamental Principle of Dynamics
• 2 Solid in Space. Efforts and Links: Power
• 3 Scalar Consequences and Movement Equations
• 4 Particular Applications
• 5 Methodological Formulary
• Bibliography
• Index
• End User License Agreement