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Essentials of dynamics and vibrations

By: Billingsley, John
Publisher: Cham, Switzerland : Springer, c2018.Description: vii, 165 p. : ill. ; 25 cm.ISBN: 9783319565163Subject(s): MathematiciansDDC classification: 531​.11 BI ES Online resources: Location Map
Summary:
Dynamic objects move in mysterious ways. Their analysis is a difficult subject involving matrices, differential equations and the complex algebra of oscillatory systems. However, in this textbook, the author draws on his long experience of designing autopilots, robots for nuclear inspection and agricultural machine guidance to present the essentials with a light touch. The emphasis is on a deep understanding of the fundamentals rather than rote-learning of techniques. The inertia tensor is presented as a key to understanding motion ranging from boomerangs to gyroscopes. Chains of transformations unravel the motion of a robot arm. To help the reader visualize motion, ranging from unbalanced rotors to vibrating systems with multiple modes and damping, there are abundant simulation examples on a linked website. These will run in any web browser, while their simple code is on open view for modification and experimentation. They show that nonlinear systems present no problems, so that friction damping can be modelled with ease. A particular problem for mechanical engineers is that the vibration topics encroach on the territory of the electrical engineer. State variables open up control theory while the solution of differential equations with sinusoidal inputs is simplified by an understanding of sine-waves as complex exponentials. The linked web site has several areas of mathematics revision to help. A final chapter pokes fun at the misrepresentation of dynamics in cinema productions.
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Item type Home library Call number Status Notes Date due Barcode Item holds
REGULAR University of Wollongong in Dubai
Main Collection 		531​.11 BI ES (Browse shelf) Available July2019 T0062723
Total holds: 0

1 Introduction
2 The Essential Mathematics
3 Kinematics and Dynamics of Particles
4 Inertia
5 Momentum
6 Balancing
7 Three Dimensional Kinematics
8 Kinematic Chains
9 Vibration 1
10 Vibration 2
11 Couples, Moments and Euler's Equations
12 Gyroscopes
13 Gears, Motors, and Mechanisms.
1. Overview
2. Particle kinematics and dynamics
3. Linear and angular momentum
4. Inertia
5. Balancing and the inertia tensor
6. Couples, moments and Euler's equations
7. Gyroscopes
8. Kinematics
9. Kinematic chains
10. Inverse kinematics
11. Vibration
12. Modes
13. Rocket science
Appendix 1: Mathematicians and operators
Appendix 2: Lagrange and Hamilton.

Dynamic objects move in mysterious ways. Their analysis is a difficult subject involving matrices, differential equations and the complex algebra of oscillatory systems. However, in this textbook, the author draws on his long experience of designing autopilots, robots for nuclear inspection and agricultural machine guidance to present the essentials with a light touch. The emphasis is on a deep understanding of the fundamentals rather than rote-learning of techniques. The inertia tensor is presented as a key to understanding motion ranging from boomerangs to gyroscopes. Chains of transformations unravel the motion of a robot arm. To help the reader visualize motion, ranging from unbalanced rotors to vibrating systems with multiple modes and damping, there are abundant simulation examples on a linked website. These will run in any web browser, while their simple code is on open view for modification and experimentation. They show that nonlinear systems present no problems, so that friction damping can be modelled with ease. A particular problem for mechanical engineers is that the vibration topics encroach on the territory of the electrical engineer. State variables open up control theory while the solution of differential equations with sinusoidal inputs is simplified by an understanding of sine-waves as complex exponentials. The linked web site has several areas of mathematics revision to help. A final chapter pokes fun at the misrepresentation of dynamics in cinema productions.

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