作者介紹
(德)阿諾德·索末菲|責編:陳亮
阿諾德·索末菲（Arnold Sommerfeld，1868-1951），Sommerfeld是德國偉大的理論物理學家、應用數學家、流體力學家、教育家、原子物理與量子物理的創始人之一。他對理論物理多個領域，包括力學、光學、熱力學、統計物理、原子物理、固體物理（包括金屬物理）等有重大貢獻，在偏微分方程、數學物理等應用數學領域也有重要貢獻。他引進了第二量子數（角量子數）、第四量子數（自旋量子數）和精細結構常數，等等。20世紀最偉大的物理學家之一Planck在獲得1918年度諾貝爾物理學獎的頒獎典禮的儀式上的演講中指出：「Sommerfeld…便可以得到一個重要公式，這個公式能夠解開氫與氫光譜的精細結構之謎，而且現在最精確的測量……一般地也能通過這個公式來解釋……這個成就完全可以和海王星的著名發現相媲美。早在人類看到這顆行星之前Leverrier就計算出它的存在和軌道。」
Sommerfeld思想深刻，研究成果影響深遠。例如，他去世后發展起來的數值廣義相對論和新近崛起的引力波理論研究中，還引用「Sommerfeld條件」，該條件在求解中發揮了重要作用。這再次彰顯了他的科學工作的巨大價值。
目錄
FOREWORD TO SOMMERFELD'S COURSE BY P. P. EWALD
PREFACE TO THE FIRST EDITION
INTRODUCTION
CHAPTER Ⅰ. MECHANICS OF A PARTICLE
1.Newton's Axioms
2.Space, Time and Reference Systems
3.Rectilinear Motion of a Mass Point
Examples:
(1)Free Fall Near Earth's Surface (Falling Stone)
(2)Free Fall From a Great Distance (Meteor)
(3)Free Fall in Air
(4)Harmonic Oscillations
(5)Collision of Two Particles
4.Variable Masses
5.Kinematics and Statics of a Single Mass Point in a Plane and in Space
(1)Plane Kinematics
(2)The Concept of Moment in Plane Statics and Kinematics
(3)Kinematics in Space
(4)Statics in Space; Moment of Force About a Point and About an Axis
6.Dynamics (Kinetics) of the Freely Moving Mass Point; Kepler Problem; Concept of Potential Energy
(1)Kepler Problem with Fixed Sun
(2)Kepler Problem Including Motion of the Sun
(3)When Does a Force Field Have a Potential?
CEAPTER Ⅱ. MECHANICS OF SYSTEMS, PRINCIPLE OF VIRTUAL WORK, ANDD'ALEMBERT'S PRINCIPLE
7.Degrees of Freedom and Virtual Displacements of a Mechanical Syatem;Holonomic and Non-holonomic Constraints
8.The Principle of Virtual Work.
9.Illustrations of the Principle of Virtual Work
(1)The Lever
(2)Inverse of the Lever: Cyclist, Bridge
(3)The Block and Tackle
(4)The Drive Mechanism of a Piston Engine
(5)Moment of a Force About an Axis and Work in a Virtual Rotation
10.D'Alembert's Principle; Introduction of Inertial Forces
11.Application of d'Alembert's Principle to the Simplest Problems
(1)Rotation of a Rigid Body About a Fixed Axis
(2)Coupling of Rotational and Translational Motion
(3)Sphere Rolling on Inclined Plane
(4)Mass Guided Along Prescribed Trajectory
12.Lagrange's Equations of the First Kind
13.Equations of Momentum and of Angular Momentum
(1)Equation of Momentum
(2)Equation of Angular Momentum
(3)Proof Using the Coordinate Method
(4)Examples
(6)General Rule on the Number of Integrations Feasible in a Closed
(5)Mass Balancing of Marine Engines Syetem
14.The Laws of Friction
(1)Static Friction
(2)Sliding Friction
CHAPTER Ⅲ. OSCILLATION PROBLEMS
15.The Simple Pendulum
16.The Compound Pendulum
Supplement: A Rule Concerning Moments of Inertia
17.The Cycloidal Pendulurm
18.The Spherical Pendulum
19.Various Types of Oscillations. Free and Forced, Damp and Undamped Oscillations
20.Sympathetic Oscillations
21.The Double Pendulum
CHAPTER Ⅳ. THE RIGID BODY
22.Kinematics of Rigid Bodies
23.Statics of Rigid Bodies
(1)The Conditions of Equilibrium
(2)Equipollence; the Reduction of Force Systems
(3)Change of Reference Point
(4)Comparison of Kinematics and Statics
Supplement: Wrenches and Screw Displacements
24.Linear and Angular Momentum of a Rigid Body. Their Connection with Linear and Angular Velocity
25.Dynamics of a Rigid Body. Survey of its Forms of Motion
(1)The Spherical Top Under No Forces
(2)The Symmetrical Top Under No Forces
(3)The Unsymmetrical Top Under No Forces
(4)The Heavy Symmetrical Top
(5)The Heavy Unsymmetrical Top
26.Euler's Equations. Quantitative Treatment of the Top Under No Forces
(1)Euler's Equations of Motion
(2)Regular Precession of the Symmetrical Top Under No Forces and Euler's Theory of Polar Fluctuations
(3)Motion of an Unsymmetrical Top Under No Forces. Examination of its Permanent Rotations as to Stability
27.Demonstration Experiments Illustrating the Theory of the Spinning Top; Practical Applications
(1)The Gyrostabilizer and Related Topics
(2)The Gyrocompass
(3)Gyroscopic Effects in Railroad Wheels and Bicycles
Supplement: The Mechanics of Billiards
(a)High and Low Shots, 158—(b) Follow Shots and Draw Shots, 159—
(c)Trajectories with " English " Under Horizontal Impact, 160—
(d)Parabolic Path Due to Shot with Vertical Component, 160
CHAPTER Ⅴ. RELATIVE MOTION
28.Derivation of the Coriolis Force in a Special Case
29.The General Differential Equations of Relative Motion
30.Free Fall on the Rotating Earth; Nature of the Gyroscopic Terms
31.Foucault's Pendulum
32.Lagrange's Case of the Three-Body Problem
CHAPTER Ⅵ. INTEGRAL VARIATIONAL PRINCIPLES OF MECHANICS AND LAGRANGE'S EQUATIONS FOR GENERALIZED COORDINATES
33.Hamilton's Principle
34.Lagrange's Equations for Generalized Coordinates
35.Examples Illustrating the Use of Lagrange's Equations
(1)The Cycloidal Pendulum
(2)The Spherical Pendulum
(3)The Double Pendulum
(4)The Heevy Symmetrical Top
36.An Alternate Derivation of Lagrange's Equations
37.The Principle of Least Action
CHAPTER Ⅶ. DIFFERENTIAL VARIATIONAL PRINCIPLES OF MECHANICS
38.Gauss' Principle of Least Constraint
39.Hertz's Principle of Least Curvature
40.A Digression on Geodesics
CHAPTER Ⅷ. THE THEORY OF HAMILTON
41.Hamilton's Equations
(1)Derivation of Hamilton's Equations from Lagrange's Equations
(2)Derivation of Hamilton's Equations from Hamilton's Principle
42.Routh's Equations and Cyclic Systems
43.The Differential Equations for Non-Holonomic Velocity Parameters
44.The Hamilton-Jacobi Equation
(1)Conservative Systems
(2)Dissipative Systems
45.Jacobi's Rule on the Integration of the Hamilton-Jacobi Equation
46.Classical and Quantum-Theoretical Treatment of the Kepler Problem
PROBLEMS
FOR CHAPTER Ⅰ
Ⅰ.1, Ⅰ.2, Ⅰ.3. Elastic collision
Ⅰ.4.Inelastic collision between an electron and an atom
Ⅰ.5.Rocket to the moon
Ⅰ.6.Water drop falling through saturated atmosphere
Ⅰ.7.Falling chain
Ⅰ.8.Falling rope
Ⅰ.9.Acceleration of moon due to earth's attraction
Ⅰ.10.The torque as vector quantity
Ⅰ.11.The hodograph of planetary motion
Ⅰ.12.Parallel beam of electrons passing through the field of an ion Envelope of the trajectories
Ⅰ.13.Elliptical trajectory under the influence of a central force directly proportional to the distance
Ⅰ.14.Nuclear disintegration of lithium
Ⅰ.15.Central collisions between neutrons and atomic nuclei; effect of a block of paraffin
Ⅰ.16.Kepler's equation
FOR CHAPTER Ⅱ
Ⅱ.1.Non-holonomic conditions of a rolling wheel
Ⅱ.2.Approximate design of a flywheel for a double-acting one-oylinder steam engine
Ⅱ.3.Centrifugal force under increased rotation of the earth
Ⅱ.4.Poggendorff's experiment
Ⅱ.5.Accelerated inclined plane
Ⅱ.6.Products of inertia for the uniform rotation of an unsyrmmetrical bodyabout an axis
Ⅱ.7.Theory of the Yo-yo
Ⅱ.8.Particle moving on the surface of a sphere
FOR CHAPTER Ⅲ
Ⅲ.1.Spherical pendulum under infinitesimal oscillations
Ⅲ.2.Position of the resonance peak of forced damped oscillations
Ⅲ.3.The galvanometer
Ⅲ.4.Pendulum under forced motion of its point of suspension
Ⅲ.5.Practical arrangement of coupled pendulums
Ⅲ.6.The oscillation quencher
FOR CHAPTER Ⅳ
Ⅳ.1.Moments of inertia of a plane mass distribution
Ⅳ.2.Rotation of the top about its principal axes
Ⅳ.3.High and low shots in a billiard game. Follow shot and draw shot
Ⅳ.4.Parabolic motion of a billiard ball
FOB CHAPTER Ⅴ
Ⅴ.1.Relative motion in a plane
Ⅴ.2.Motion of a particle on a rotating straight line
Ⅴ.3.The sleigh as the simplest example of a non-holonomic system
FOB CHAPTER Ⅵ
Ⅵ.1.Example illustrating Hamilton's principle
Ⅵ.2.Relative motion in a plane and motion on a rotating straight line
Ⅵ.3.Free fall on the rotating earth and Foucault's pendulum
Ⅵ.4."Wobbling" of a cylinder rolling on a plane support
Ⅵ.5.Differential of an automobile
HINTS FOR SOLVING THE PROBLEMS
INDEX
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