This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes.

Contents
Generalized formulations of parabolic and hyperbolic problems
Variational principles in linear elasticity
Variational statements in structural mechanics
Ritz method for initial-boundary value problems
Variational and projection techniques with semi-discretization
Integrodifferential approach to eigenvalue problems
Spatial vibrations of elastic beams with convex cross-sections
Double minimization in optimal control problems
Semi-discrete approximations in inverse dynamic problems
Modeling and control in mechatronics

• Preface 8
• Basic notation 12
• Contents 14
• 1. Introduction 20
• 2. Generalized formulations of parabolic and hyperbolic problems 28
• 3. Variational principles in linear elasticity 50
• 4. Variational statements in structural mechanics 72
• 5. Ritz method for initial-boundary value problems 90
• 6. Variational and projection techniques with semi-discretization 132
• 7. Integrodifferential approach to eigenvalue problems 148
• 8. Spatial vibrations of elastic beams with convex cross-sections 184
• 9. Double minimization in optimal control problems 216
• 10. Semi-discrete approximations in inverse dynamic problems 248
• 11. Modeling and control in mechatronics 278
• A. Vectors and tensors 294