Classical and Analytical Mechanics
Theory, Applied Examples, and Practice
- 1st Edition - April 8, 2021
- Imprint: Elsevier
- Author: Alexander S. Poznyak
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 8 9 8 1 6 - 4
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 8 9 8 8 9 - 8
Classical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electrome… Read more
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Request a sales quoteClassical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electromechanical systems. It includes rigorous mathematical and physical explanations while maintaining an interdisciplinary engineering focus. Applied problems and exercises in mechanical, mechatronic, aerospace, electrical, and control engineering are included throughout and the book provides detailed techniques for designing models of different robotic, electrical, defense, and aerospace systems. The book starts with multiple chapters covering kinematics before moving onto coverage of dynamics and non-inertial and variable mass systems. Euler’s dynamic equations and dynamic Lagrange equations are covered next with subsequent chapters discussing topics such as equilibrium and stability, oscillation analysis, linear systems, Hamiltonian formalism, and the Hamilton-Jacobi equation. The book concludes with a chapter outlining various electromechanical models that readers can implement and adapt themselves.
- Bridges theory and practice by providing readers techniques for solving common problems through mechanical, electrical, and electromechanical models alongside the underlying theoretical foundations
- Describes variable mass, non-inertial systems, dynamic Euler’s equations, gyroscopes, and other related topics
- Includes a broad offering of practical examples, problems, and exercises across an array of engineering disciplines
Researchers and graduate students in mechanical, aerospace, electrical, mechatronics, and control engineering. Professional mechanical, mechatronic, electrical and aerospace engineers
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- List of figures
- List of tables
- About the author
- Preface
- Notation
- Scalars
- Vectors
- Matrices
- Functions
- Derivatives
- Quaternion
- Quadratic forms
- Introduction
- Bibliography
- 1: Kinematics of a point
- Abstract
- 1.1. Products of vectors
- 1.2. Generalized coordinates
- 1.3. Kinematics in generalized coordinates
- 1.4. Movement in the cylindrical and spherical coordinate systems
- 1.5. Normal and tangential accelerations
- 1.6. Some examples
- 1.7. Exercises
- 2: Rigid body kinematics
- Abstract
- 2.1. Angular velocity
- 2.2. Complex movements of the rigid body
- 2.3. Complex movement of a point
- 2.4. Examples
- 2.5. Kinematics of a rigid body rotation
- 2.6. Rotations and quaternions
- 2.7. Differential kinematic equations (DKEs)
- 2.8. Exercises
- 3: Dynamics
- Abstract
- 3.1. Main dynamics characteristics
- 3.2. Axioms or Newton's laws
- 3.3. Force work and potential forces
- 3.4. Virial of a system
- 3.5. Properties of the center of mass
- 3.6. “King/König/Rey” theorem
- 3.7. Movements with friction
- 3.8. Exercises
- 4: Non-inertial and variable-mass systems
- Abstract
- 4.1. Non-inertial systems
- 4.2. Dynamics of systems with variable mass
- 4.3. Exercises
- 5: Euler's dynamic equations
- Abstract
- 5.1. Tensor of inertia
- 5.2. Relative kinetic energy and impulse momentum
- 5.3. Some properties of inertial tensors
- 5.4. Euler's dynamic equations
- 5.5. Dynamic reactions caused by the gyroscopic moment
- 5.6. Exercises
- Bibliography
- 6: Dynamic Lagrange equations
- Abstract
- 6.1. Mechanical connections
- 6.2. Generalized forces
- 6.3. Dynamic Lagrange equations
- 6.4. Normal form of Lagrange equations
- 6.5. Electrical and electromechanical models
- 6.6. Exercises
- 7: Equilibrium and stability
- Abstract
- 7.1. Definition of equilibrium
- 7.2. Equilibrium in conservative systems
- 7.3. Stability of equilibrium
- 7.4. Unstable equilibria in conservative systems
- 7.5. Exercises
- Bibliography
- 8: Oscillations analysis
- Abstract
- 8.1. Movements in the vicinity of equilibrium points
- 8.2. Oscillations in conservative systems
- 8.3. Several examples of oscillation analysis
- 8.4. Exercises
- Bibliography
- 9: Linear systems of second order
- Abstract
- 9.1. Models governed by second order differential equations
- 9.2. Frequency response
- 9.3. Examples
- 9.4. Asymptotic stability
- 9.5. Polynomial robust stability
- 9.6. Exercises
- Bibliography
- 10: Hamiltonian formalism
- Abstract
- 10.1. Hamiltonian function
- 10.2. Hamiltonian canonical form
- 10.3. First integrals
- 10.4. Some properties of first integrals
- 10.5. Exercises
- 11: The Hamilton–Jacobi equation
- Abstract
- 11.1. Canonical transformations
- 11.2. The Hamilton–Jacobi method
- 11.3. Hamiltonian action and its variation
- 11.4. Integral invariants
- 11.5. Canonicity criteria
- 11.6. The Hamilton–Jacobi equation
- 11.7. Complete integral of the Hamilton–Jacobi equation
- 11.8. On relations with optimal control
- 11.9. Exercises
- Bibliography
- 12: Collection of electromechanical models
- Abstract
- 12.1. Cylindrical manipulator (2-PJ and 1-R)
- 12.2. Rectangular (Cartesian) robot manipulator
- 12.3. Scaffolding type robot manipulator
- 12.4. Spherical (polar) robot manipulator
- 12.5. Articulated robot manipulator 1
- 12.6. Universal programmable manipulator
- 12.7. Cincinnati Milacron T3 manipulator
- 12.8. CD motor, gear, and load train
- 12.9. Stanford/JPL robot manipulator
- 12.10. Unimate 2000 manipulator
- 12.11. Robot manipulator with swivel base
- 12.12. Cylindrical robot with spring
- 12.13. Non-ordinary manipulator with shock absorber
- 12.14. Planar manipulator with two joints
- 12.15. Double “crank-turn” swivel manipulator
- 12.16. Robot manipulator of multicylinder type
- 12.17. Arm manipulator with springs
- 12.18. Articulated robot manipulator 2
- 12.19. Maker 110
- 12.20. Manipulator on a horizontal platform
- 12.21. Two-arm planar manipulator
- 12.22. Manipulator with three degrees of freedom
- 12.23. CD motor with load
- 12.24. Models of power converters with switching-mode power supply
- 12.25. Induction motor
- Bibliography
- Bibliography
- Index
- Edition: 1
- Published: April 8, 2021
- Imprint: Elsevier
- No. of pages: 524
- Language: English
- Paperback ISBN: 9780323898164
- eBook ISBN: 9780323898898
AP
Alexander S. Poznyak
Alexander Poznyak is Professor and Department Head of Automatic Control at CINESTAV of IPN in Mexico. He graduated from Moscow Physical Technical Institute in 1970, and earned Ph.D. and Doctoral Degrees from the Institute of Control Sciences of Russian Academy of Sciences in 1978 and 1989, respectively. He has directed 43 Ph.D. theses, and published more than 260 papers and 14 books.
Affiliations and expertise
Professor and Department Head of Automatic Control, CINESTAV of IPN, MexicoRead Classical and Analytical Mechanics on ScienceDirect