Classical mechanics : an undergraduate text /
R. Douglas Gregory.
- Cambridge, New York : Cambridge University Press, c2006.
- xii, 596 p. : ill. ; 26 cm.
CONTENTS
1 The algebra and calculus of vectors
1.1 Vector and vector quantities 1.2 Linear operation 1.3 The scalar product 1.4 The vector product
2 Velocity, acceleration and scalar angular velocity
2.1 Straight line motion of a particle 2.2 General motion of particle 2.3 Particle motion in polar co-ordinates etc
3 Newton's laws of motion and the law of gravitation
3.1 Newton's law of motion 3.2 Inertial frames and the law of inertial 3.3 The law of mutual interaction; mas and force 3.4 The law of multiple interactions etc
4 Problems in particle dynamics
4.1 Rectilinear motion in a force field 4.2 Constrained rectilinear motion 4.3 Motion through a resisting medium 4.4 projectiles etc
5 Linear oscillations
5.1 Body on spring 5.2 Classical simple harmonic motion 5.3 Damped simple harmonic motion 5.4 Driven motion etc
6 Energy conservation
6.1 The energy principle 6.2 Energy conservation 6.3 General features of rectilinear motion etc
7 Orbits in a central field
7.1 The one body problem- newton's equations 7.2 General nature of orbital motion 7.3 The path equation 7.4 Nearly circular orbits etc
8 Non-linear oscillations and phase space
8.1 Periodic non-linear oscillations 8.2 The phase plane 8.3 The phase plane in dynamics etc
9 The energy principle
9.1 Configurations and degrees of freedom 9.2 The energy principle for a system 9.3 Energy conservation 9.4 Kinetic energy of rigid body
10 The linear momentum principle
10.1 Linear momentum 10.2 The linear momentum principle 10.3 Motion of the centre of mass etc
11 The angular momentum
11.1 The momentum of a force 11.2 Angular momentum 11.3 Angular momentum of a rigid body 11.4 The angular momentum principle etc
12 Lagrange's equations and conservation principles
12.1 Constraints and constraint forces 12.2 Generalized coordinates 12.3 Configuration space etc
13 The calculus of variations and Hamilton's principle
13.1 Some typical minimisation problems 13.2 The Euler-Lagrange equation 13.3 Variational principle etc
14 Hamilton's Equations and phase space
14.1 Systems of first order ODEs 14.2 Legendre transforms 14.3 Hamilton's equations etc
15 The general theory of small oscillations
15.1 Stable equilibrium and small oscillations 15.2 The approximate forms of T and V 15.3 The general theory of normal modes etc
16 Vector angular velocity and rigid body kinematics
16.1 Rotation about a fixed axis 16.2 General rigid body kinematics
17 Rotating reference frames
17.1 Transformation formulae 17.2 Particle dynamics in a non-inertial frame 17.3 Motion relative to the earth 17.4 Multi-particle system in non-inertial frame
18 Tensor algebra and the inertial tensor
18.1 Orthogonal transformations 18.2 Rotated and reflected coordinates system 18.3 Scalars, vectors and tensors 18.4 Tensor algebra etc
19 Problems in rigid body dynamics
19.1 Equations of rigid body dynamics 19.2 Motion of 'spheres' 19.3 The snooker ball 19.4 Free motion of bodies with axial symmetry 19.5 The spinning top etc
Includes bibliography : p. 589 - 590 . _ Index : p. 591 - 596.