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Classical Mechanics

Part of the Advances in Mechanics and Mathematics Book Series (volume 29)

DOI: 10.1007/978-1-4614-3740-6

ISBN: 978-1-4614-3739-0

Publisher: Springer New York - Springer Journals

May 12, 2012

1 - 10 of 11 Chapters

LitStream

Chapter 1Particle Dynamics, Material System Dynamics and Rigid-Body Motion About a Point

Awrejcewicz, Jan

Pages: 1 –68

[Let us return to Chap. 1 of [1], where Newton’s laws were introduced. The second law formulates the relation between the acceleration of motion of a particle and the force acting on it. However, it turns out that only in certain cases is the force F acting on this particle independent of the...
LitStream

Chapter 2Mathematical and Physical Pendulum

Awrejcewicz, Jan

Pages: 69 –106

[A particle of mass m connected by a rigid, weightless rod (or a thread) of length l to a base by means of a pin joint that can oscillate and rotate in a plane we call a mathematical pendulum (Fig. 2.1).]
LitStream

Chapter 3Statics and Dynamics in Generalized Coordinates

Awrejcewicz, Jan

Pages: 107 –206

[We will consider a discrete (lumped) material system (DMS) in Euclidean space E3 composed of N particles of masses m1, m2, …, mN (see [1]), presented in Fig. 3.1, which, as mentioned earlier, will be called a discrete mechanical system.]
LitStream

Chapter 4Classic Equations of Dynamics

Awrejcewicz, Jan

Pages: 207 –247

[Let us return to Lagrange’s equations of the second kind, which, for the system of N degrees of freedom loaded exclusively with potential forces, take the form]
LitStream

Chapter 5Theory of Impact

Awrejcewicz, Jan

Pages: 249 –269

[So far we have considered problems concerning the statics and dynamics of discrete (lumped) and continuous material systems when forces of action and reaction act upon these systems in a continuous fashion for the entire duration of a process. On the other hand, it is known that changes in...
LitStream

Chapter 6Vibrations of Mechanical Systems

Awrejcewicz, Jan

Pages: 271 –322

[Vibration theory belongs to well-developed branches of mechanics and physics. It cannot be understood without a good command of the fundamentals of mathematics. A large body of literature exists that is devoted to the theory of vibrations of discrete and continuous systems; it is not cited here...
LitStream

Chapter 7Elements of Dynamics of Planets

Awrejcewicz, Jan

Pages: 323 –339

[For a long time the structure of the universe has aroused admiration and dread, and for a long time people have tried to explain the phenomena of the cosmos. However, not much has changed for hundreds of years in this field of human activity.]
LitStream

Chapter 8Dynamics of Systems of Variable Mass

Awrejcewicz, Jan

Pages: 341 –357

[So far we have considered DMSs and CMSs in which masses of particles mn and their number have not changed. In nature and technology, however, phenomena are commonly known where the number of particles of a system or their mass change over time.]
LitStream

Chapter 9Body and Multibody Dynamics

Awrejcewicz, Jan

Pages: 359 –432

[The kinematics and statics of particles of a body supported by a thrust bearing and radial bearing have already been considered in Chaps. 2 and 5 of [1].]
LitStream

Chapter 10Stationary Motions of a Rigid Body and Their Stability

Awrejcewicz, Jan

Pages: 433 –441

[Let us consider a scleronomic mechanical system described by the system of differential equations 10.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

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