质点和刚体分析动力学专论
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作者惠特克(E. T. Whittader)著
出版社世界图书出版公司北京公司
ISBN9787510026973
出版时间2017-01
装帧平装
开本其他
定价79元
货号8945861
上书时间2024-12-13
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作者简介
Whittaker,E.T.是英国著名数学家,他的名著《质点和刚体分析动力学专论》目次包括：动力学初步；运动方程；积分理论；质点动力学解决方法；刚体的动力学说明；刚体动力学解决方法；振动理论；非完整系统和耗能系统；最小作用量和最小曲率原理；Hamilton系统和积分不变量；动力学转变理论；动力学系统的积分问题；三种刚体问题的化简；Bruns和Poincare定理；一般轨道理论；级数积分。
目录
Foreword by Sir William McCrea， FIRS
Preface to the fourth edition
CHAPTER Ⅰ KINEMATICAL PRELIMINARIES
SECTION
1.The displacements of rigid bodies
2.Eulers theorem on rotations about a point
3.The theorem of Rodrigues and Hamilton
4.The composition of equal and opposite rotations about parallel axes
5.Chasles theorem on the most general displacement of a rigid body
8.Halphens theorem on the composition of two general displacements
7.Analytic representation of a displacement
8.The composition of small rotations
9.Eulers parametric specification of rotations round a point
10.The Eulerian angles
11.Connexion of the Eulerian angles with the parameters ξ，η，ζ，x
12.The connexion of rotations with homographies：the Cayley—Klein paramctors
13.Vectors
14.Velocity and acceleration ； their vectorial character
15.Angular velocity ； its vectorial character
16.Determinstion of the components of angular veloeity of a system in terms of the Eulerian angles， and of the symmetrical parameters
17.Time—flux of a vector whose components relative to moving axes are given
18.Spe resolutions of the velocity and acoeleration
NISCELLANEOUS EXAMPLES
CHAPTER Ⅱ THE EQUATIONS OF MOTION
19.The ideas of rest and motion
20.The laws which determine motion
21.Force
22.Work
23.Forees which do no work
24.The coordinates of a dynamical system
25.Holonomic and non—holonomic systems
SECTION
26.Lagranges form of tho equations of motion ofa holonomic system
27.Conservative forces ； the kinetic potential
28.The explicit form of Lagranges equations
29.Motion of a system which is constrained to rotate uniformly round an axis
30.The Lagrangian equations for quasi—coordinates
31.Forces derivable from a potential.function which involves the velocities
32.Initial motions
33.Similarity in dynamical systems
34.Motion with reversed forces
35.Impulsive motion
36.The Lagrangian equations of impulsive motion
MISCELLANEOUS EXAMPLES
CHAPTER Ⅲ PRINCIPLES AVAILABLE FOR THE INTEGRATION
37.Problems which are soluble by quadratures
38.Systems with ignorable coordinates
39.Spe cases of iguoration ； integrals of momentum and angular momentum
40.The general theorem of angular momentum
41.The energy equation
42.Reduction of a dynamical problem to a problem with fewer degrees of freedom， by means of the energy equation
43.Separation of the variables ； dynamical systems of Liouvilles type
MISCELLANEOUS EXAMPLES
CHAPTER Ⅳ THE SOLUBLE PROBLEMS OF PARTICLE DYNAMICS
41.The particle with one degree of freedom ； the pendulum
45.Motion in a moving tube
46.Motion of two interacting free perticles
47.Central forces in general ： Hamiltons theorem
48.The integrable cases of central forces； problems soluble in terms of circular and elliptic functions
49.Motion under the Newtonian law
50.The mutual transformation of fields of ecntral force and fields of parallcl force
51.Bonnets theorem
52.Determination of the most general field of force under which a given curve or family of curves can be described
53.The problem of two eentres of gravitation
54.Motion on a surface
55.Motion on a sur face of revolution ； cases soluble in terms of circular and elliptic functions
56.Joukovskys theorem
MISCELLANEOUS EXAMPIMS
CHAPTER Ⅴ THE DYNAMICAL SPECIFICATION OF BODIES
SECTION
57.Definitions
58.The moments of inertia of some simple bodies
59.Derivation of the moment of inertia about anyaxis when the moment of inertia about a parallel axis through the centre of gravity is known
60.Connexion between moments of inertia with respect to different sets of axes through the same origin
61.The principal axes of inertia ； Cauchys momental ellipsoid
62.Caleulation of the angular momentum of a moving rigid body
63.Calculation of the kinetic energy of a moving rigid body
64.Independence of the motion of the centre of gravity and the motion relative to it
MISCELLANEOUS EXAMPLES
CHAPTER Ⅵ THE SOLUBLE PROBLEMS OF RIGID DYNAMICS
65.The motion of systems with one degree of freedom ； motion round a fixed axis， etc.
66.The motion of systems with two degrees of freedom
67.Initial motions
88.The motion of systems with three degrees of freedom
69.Motion of a body about a fixed point under no forces
70.Poinsots kinematical representation of the motion； the polhode and herpolhode
71.Motion of a top on a perfectly rough plane； determination of the Eulerian angle θ
72.Determination of the remaining Eulerian angles， and of the Cayley—Klein parameters； the spherical top
73.Motion of a top on a perfectly smooth plane
74.Kowalevskis top
75.Impulsive motion
MISCELLANEOUS EXAMPLES
CHAPTER Ⅶ THEORY OF VIBRATIONS
76.Vibrations about equilibrium
77.Normal eoordinates
78.Sylvesters theorem on the reality of the roots of the determinantal equation
79.Solution of the differential equations； the periods； stability.
80.Examples of vibrations about equilibrium
81.Effect of a new constraint on the periods of a vibrating system
82.The stationary character of normal vibrations
83.Vibrations about steady motion
84.The integration of the equations
85.Examples of vibrations about steady motion
86.Vibrations of systems involving moving constraints
MISCELLANEOUS EXAMPLES
CHAPTER Ⅷ NON—HOLONOMIC SYSTEMS.DISSIPATIVE SYSTEMS
SECTION
87.Lagranges equations with undetermined multipliers
88.Equations of motion referred to axes moving in any manner
89.Application to spe non—holonomic problems
90.Vibrations of non—holonomic systems
91.Dissipative systems； frictional forces
92.Resisting forces which depend on the velocity
93.Rayleighs dissipation—function
94.Vibrations
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