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3D Motion of Rigid Bodies

Part of the Studies in Systems, Decision and Control Book Series (volume 191)

DOI: 10.1007/978-3-030-04275-2

ISBN: 978-3-030-04274-5

Publisher: Springer International Publishing - Springer Journals

Dec 7, 2018

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Mathematic Foundations

Olguín Díaz, Ernesto

Pages: 3 –100

[Linear algebra is not only related with matrices and matrix operations which define the algebraic matrix theory, but also with linear operators which relate vectors spaces. While matrices have a more algebraic point of view to these algebras, operators and vectors spaces have a more geometric...
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Classical Mechanics

Olguín Díaz, Ernesto

Pages: 101 –144

[Newton’ mechanics is the set of motion expression for either a particle or a group of particles which are the result of his widely known motion laws. While the first two laws gives rise to some important facts only in the mechanics of particles, the third one is essential for the extension of...
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Rigid Motion

Olguín Díaz, Ernesto

Pages: 147 –183

[The rigid motion refers to the motion of rigid bodies. This means the use of Galileo transformations to describe the displacement of a body with respect to a given reference frame, and a rotations from which both linear and angular velocities can be derived. These expressions are needed in the...
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Attitude Representations

Olguín Díaz, Ernesto

Pages: 185 –230

[In previous Chapter, there has been presented a set of solutions for complex rotation using 3 concatenated basic rotation. All of this solutions, using three rotation angles about some defined principal axis of either: the base frame or the current frame, are the so-called Euler angles. In...
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Dynamics of a Rigid Body

Olguín Díaz, Ernesto

Pages: 231 –271

[If D’Alembert principle is used on the particles of a rigid body, the principle would state: When a rigid body that is in equilibrium (either static of dynamic) is subject to virtual compatible displacements, the total virtual work of all external forces is zero; and conversely, if the total...
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Spacial Vectors Approach

Olguín Díaz, Ernesto

Pages: 273 –305

[By definition any vector has a magnitude and a direction. For some physical vectors this information is enough for their definition. For example the angular velocity of a rigid body or the 3-D force applied to it. In any case neither the angular kinematics nor the translational dynamic motion do...
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Lagrangian Formulation

Olguín Díaz, Ernesto

Pages: 307 –328

[The dynamic equation of motion of a multi-particle conservative system is obtained using either D’Alembert-Lagrange equation (2.62) or the General Euler-Lagrange (2.76) which in both cases would get the form given in (2.78): \documentclass[12pt]{minimal} \usepackage{amsmath}...
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Model Reduction Under Motion Constraint

Olguín Díaz, Ernesto

Pages: 331 –369

[The most common analysis assumes that a motion restriction enforces some coordinates to remain at rest, with no displacement. This non-displacement assumption means a lack of work in the restricted direction, known as the virtual work principle, which can be stated as follows:...

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