Movement equations. 1, Location, kinematics and kinetics / Michel Borel, Georges Vénizélos.

Format:

Book

Author/Creator:

Borel, Michel, author.

Vénizélos, Georges, author.

Series:

Mechanical engineering and solid mechanics series ; v. 1.

Mechanical engineering and solid mechanics series. Non-deformable solid mechanics set ; volume 1

Language:

English

Subjects (All):

Motion--Mathematical models.

Motion.

Kinematics--Mathematical models.

Kinematics.

Mechanics--Mathematical models.

Mechanics.

Physical Description:

1 online resource (278 pages) : illustrations (some color)

Edition:

1st ed.

Place of Publication:

Hoboken, New Jersey : ISTE Ltd/John Wiley and Sons Inc, 2016.

Summary:

The set of books on Mechanical Engineering and Solid Mechanics, of which this book is the first volume, is an essential tool for those looking to develop a rigorous knowledge of the discipline, whether students, professionals (in search of an approach to a problem they are dealing with), or anyone else interested. This volume deals with the elements required for establishing the equations of motion when dealing with solid bodies. Chapter 1 focuses on the systems of reference used to locate solid bodies relative to the observer, and demonstrates how to describe their position, orientation, and evolution during their motion. Chapter 2 introduces descriptors of motion such as velocity and acceleration, and develops the concept of torsor notation in relation to these descriptors. Finally, Chapter 3 concerns the notions of mass and inertia, as well as the kinetic torsor and dynamic torsor which consolidate the kinematic and kinetic aspects in a single concept.

Contents:

Cover

Titile Page

Copyright

Contents

Introduction

Table of Notations

1. Location of Solid Bodies

1.1. The notion of system of reference

1.2. Frame of reference

1.2.1. Setting up a frame of reference

1.2.2. Various types of frames of reference

1.3. Location of a solid body

1.3.1. The principle of locating a solid

1.3.2. Location parameters of a solid

1.3.3. Coordinates of the position vector

1.3.4. Exercises

1.4. Positioning of a system of reference connected to a solid

1.4.1. Several examples of location systems of reference

1.4.2. General location parameters

1.4.3. Euler angles

1.4.4. Changes of basis in the Euler representation

1.4.5. Exercises

1.5. Vector rotation Rū,α

1.5.1. Exercises

1.6. Other exercises

1.6.1. Exercise 7 - Location of an airplane - Euler angles

1.6.2. Exercise 8 - Vector rotation

1.6.3. Exercise 9 - Vector rotation

1.6.4. Exercise 10 - Vector rotation

2. Solid Kinematics

2.1. Generalities on moving solids

2.1.1. Concept of a rigid material system

2.1.2. Notion of time

2.1.3. Kinematic components of a solid

2.2. Kinematics of a material point

2.2.1. Position vector

2.2.2. Trajectory of a material point in a reference frame

2.2.3. Velocity of a material point in a reference frame

2.2.4. Components of the velocity vector or velocity

2.2.5. Derivative of a vector in a basis

2.2.6. Acceleration vector of a material point in a reference frame

2.2.7. Exercises

2.3. Velocity field associated with the motion of the rigid solid

2.3.1. Fundamental formula for the velocity

2.3.2. Use of matrix notation

2.3.3. Velocity-distributing torsor

2.3.4. Partial distributing

2.4. Acceleration field of the rigid solid

2.4.1. Derivative in relation to the time of the rate of rotation.

2.4.2. Derivation of a vector of the solid

2.4.3. Fundamental formula of acceleration

2.4.4. Matrix notation of the vectorial product

2.4.5. Exercises

2.5. Motion with fixed plane

2.5.1. Position of the problem

2.5.2. Instantaneous rotation center

2.5.3. Fixed and mobile centroids of the motion

2.5.4. The instantaneous center of rotation on the fixed centroid and on the movable centroid

2.5.5. Physical interpretation of the notions of fixed centroid and mobile centroid

2.5.6. Exercises

2.6. Combining motions within a mobile frame of reference

2.6.1. Position of the problem

2.6.2. Trajectory of a material point in the different frames

2.6.3. Combination of velocities

2.6.4. Combination of accelerations

2.6.5. Exercises

2.7. Relative motion of two rigid solids in contact

2.7.1. Position of the problem

2.7.2. Velocity-distributing torsors

2.7.3. Characterization of motions

2.7.4. Nature of the contact between (S1) and (S2)

2.7.5. Exercises

2.8. Other exercises

2.8.1. Exercise 21 - Motion with fixed plane

2.8.2. Exercise 22 - Combination of motions

2.8.3. Exercise 23 - Kinematics of contact in a system

3. Kinetics of Solid Bodies

3.1. The mass of a continuous mechanical set (D)

3.1.1. The notion of measure on a continuous mechanical set

3.1.2. The volume and the mass of a continuous mechanical set

3.2. Center of the measure of μ on (D)

3.2.1. Definition

3.2.2. Uniqueness of the center of measure

3.2.3. Center of measure of two disjoint sets

3.2.4. Coordinates of the center of measure in a system of reference ‹λ›

3.3. Interpretation of the notion of center of measure

3.4. Kinetic torsor of a mechanical set (D)

3.4.1. Definition - linear momentum

3.4.2. Kinetic torsor {pλs} of a rigid solid body

3.4.3. Inertia operator Ios (S\m).

3.4.4. Kinetic torsor and change of basis

3.5. Dynamic torsor of a mechanical set (D)

3.5.1. Definition

3.5.2. Dynamic torsor of the rigid solid body (S)

3.6. Kinetic energy of a mechanical set (D)

3.6.1. Definition

3.6.2. Kinetic energy of the free rigid solid body (S)

3.6.3. Derivatives of the kinetic energy - Lagrangian

3.3.4. Exercises

3.6.5. Kinetic energy of a constrained solid

3.7. Partition of a continuous mechanical set (D)

Bibliography

Index

Other titles from iSTE in Mechanical Engineering and Solid Mechanics

EULA.

Notes:

Description based on print version record.

ISBN:

9781119361442

1119361443

9781119361459

1119361451

9781119361435

1119361435

OCLC:

958936756