10.6.3 Some Examples of the Functionals with Parallel-Type
Inner Product Tensors and Hamiltonian Operators . . . . 694
10.6.4 The Euler Equations of the Functionals
with Parallel-Type Inner Product Tensors
and the Hamiltonian Operator Trains . . . . . . . . . . . . . . 704
10.6.5 Other Euler Equations of the Functionals
with Parallel-Type Inner Product Tensors
and the Hamiltonian Operators . . . . . . . . . . . . . . . . . . 708
10.7 Variational Problems of Functionals with Series-Type Inner
Product Tensors and Hamiltonian Operators . . . . . . . . . . . . . . . 716
10.7.1 Variational Formula Derivations of Gradients,
Divergences and Rotations of Series-Type Inner
Product Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716
10.7.2 The Euler Equations and Natural Boundary
Conditions of the Functionals with Series-Type Inner
Product Tensors and Hamiltonian Operators . . . . . . . . . 720
10.7.3 The Euler Equations of the Functionals
with Series-Type Inner Product Tensors
and the Hamiltonian Operator Trains . . . . . . . . . . . . . . 726
10.7.4 Other Euler Equations of the Functionals
with Series-Type Inner Product Tensors
and the Hamiltonian Operators . . . . . . . . . . . . . . . . . . 730
10.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
10.9 Introduction to the Famous Scientists . . . . . . . . . . . . . . . . . . . . 737
Appendix: All Solutions to the Problems. . . . . . . . . . . . . . . . . . . . . . . . . . 751
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 973
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979
Contents
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