Methods of differential geometry in classical field theories : k-symplectic and k-cosymplectic approaches
著者
書誌事項
Methods of differential geometry in classical field theories : k-symplectic and k-cosymplectic approaches
World Scientific, c2016
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注記
Includes bibliographical references (p. 195-204) and index
内容説明・目次
内容説明
This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism.It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject.
目次
- A Review of Hamiltonian and Lagrangian Mechanics: Hamiltonian and Lagrangian Mechanics
- k-Symplectic Formulation of Classical Field Theories: k-Symplectic Geometry
- k-Symplectic Formalism
- Hamiltonian Classical Field Theory
- Hamilton-Jacobi Theory in k-Symplectic Field Theories
- Lagrangian Classical Field Theories
- Examples
- k-Cosymplectic Formulation of Classical Field Theories: k-Cosymplectic Geometry
- k-Cosymplectic Formalism
- Hamiltonian Classical Field Theories
- Hamilton-Jacobi Equation
- Lagrangian Classical Field Theories
- Examples
- k-Symplectic Systems versus Autonomous k-Cosymplectic Systems
- Relationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism: Multisymplectic Formalism
- Appendices: Symplectic Manifolds
- Cosymplectic Manifolds
- Glossary of Symbols
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