10.8 Conclusions
737
(3) Through some classical examples, the correctness of obtained Euler equations
and the natural boundary conditions are verified, meanwhile the correctness of
the used methods and derivation processes are also verified;
(4) Making use of the relative concepts of the Hamiltonian operator trains, it is
very convenient to obtain the Euler equations and the corresponding natural
boundary conditions of a functional;
(5) The variational problems of the tensor functional with Hamiltonian operators in
essence are the operations of the adjoint operators in the Hilbert space, especially
for the rotation operator of them, it is an operation of self-adjoint operator in
the Hilbert space.
(6) For other similar functionals with the scalar, vector, tensor and Hamiltonian
operators, using the methods posed by this chapter, the corresponding Euler
equations and natural boundary conditions all can be obtained.
10.9 Introduction to the Famous Scientists
Coulomb (Charles–Augustin de. 1736.6.14–1806.8.23) French physicist. Born in
Angoulême, Angoumois, died in Paris. Graduated from École royale du génie de
Mézières in 1761. Served in the Caribbean Martinique and so on since 1764, served
as a military engineer building fort. Returned home in 1772, returned to Paris in
1772. Invented the torsion balance in 1777. His paper Théorie des Machines Simples
was awarded the prize of the Franch Academy of Science in 1781, and was elected
a member of the Franch Academy of Science in that year. Proposed the Coulomb’s
law in 1785. Was appointed inspector of public instruction in 1802. In honour of
the Coulomb’s contribution to the electromagnetism the international unit of electric charge was named the Coulomb. His research interest was very extensive,
made achievements in mechanics of materials, structural mechanics, electromagnetism and friction theory etc. aspects. Because he was good at dawing theory from
the engineering practice, was acclaimed as a great engineer of Europe in the eighteenth century. The works had Essai sur une application des règles des maximis et
minimis à quelques problèmes de statique relatifs à l’architecture (1776), Recherches
théoriques et expérimentales sur la force de torsion et sur l’élasticité des fils de metal
(1884), Sur l’électricité et le magnétisme (7 volumes, 1785–1789) and Théorie des
machines simples, en ayant égard au frottement de leurs parties et à la roideur des
cordages (1789) etc.
Ampère (Andrè Marie, 1775.1.22–1836.6.10) French mathematician and physicist.
Born in Lyon, died in Marseille. Was appointed a professor of physics and chemistry
at the École Centrale in Bourg–en–Bresseof. Served as a professor of mathematics at
the École Polytechnique in 1809. Was elected a member of mathematics department
of the new Institut Impérial in 1814. Presided over the philosophy lectures at the
University of Paris in 1819, served as an assistant professor of astronomy in 1820.
Became the prestigious chair in experimental physics at the Collège de France in
1824. Was elected a member of the Royal Society in 1827. Was also a mumber of the
737
(3) Through some classical examples, the correctness of obtained Euler equations
and the natural boundary conditions are verified, meanwhile the correctness of
the used methods and derivation processes are also verified;
(4) Making use of the relative concepts of the Hamiltonian operator trains, it is
very convenient to obtain the Euler equations and the corresponding natural
boundary conditions of a functional;
(5) The variational problems of the tensor functional with Hamiltonian operators in
essence are the operations of the adjoint operators in the Hilbert space, especially
for the rotation operator of them, it is an operation of self-adjoint operator in
the Hilbert space.
(6) For other similar functionals with the scalar, vector, tensor and Hamiltonian
operators, using the methods posed by this chapter, the corresponding Euler
equations and natural boundary conditions all can be obtained.
10.9 Introduction to the Famous Scientists
Coulomb (Charles–Augustin de. 1736.6.14–1806.8.23) French physicist. Born in
Angoulême, Angoumois, died in Paris. Graduated from École royale du génie de
Mézières in 1761. Served in the Caribbean Martinique and so on since 1764, served
as a military engineer building fort. Returned home in 1772, returned to Paris in
1772. Invented the torsion balance in 1777. His paper Théorie des Machines Simples
was awarded the prize of the Franch Academy of Science in 1781, and was elected
a member of the Franch Academy of Science in that year. Proposed the Coulomb’s
law in 1785. Was appointed inspector of public instruction in 1802. In honour of
the Coulomb’s contribution to the electromagnetism the international unit of electric charge was named the Coulomb. His research interest was very extensive,
made achievements in mechanics of materials, structural mechanics, electromagnetism and friction theory etc. aspects. Because he was good at dawing theory from
the engineering practice, was acclaimed as a great engineer of Europe in the eighteenth century. The works had Essai sur une application des règles des maximis et
minimis à quelques problèmes de statique relatifs à l’architecture (1776), Recherches
théoriques et expérimentales sur la force de torsion et sur l’élasticité des fils de metal
(1884), Sur l’électricité et le magnétisme (7 volumes, 1785–1789) and Théorie des
machines simples, en ayant égard au frottement de leurs parties et à la roideur des
cordages (1789) etc.
Ampère (Andrè Marie, 1775.1.22–1836.6.10) French mathematician and physicist.
Born in Lyon, died in Marseille. Was appointed a professor of physics and chemistry
at the École Centrale in Bourg–en–Bresseof. Served as a professor of mathematics at
the École Polytechnique in 1809. Was elected a member of mathematics department
of the new Institut Impérial in 1814. Presided over the philosophy lectures at the
University of Paris in 1819, served as an assistant professor of astronomy in 1820.
Became the prestigious chair in experimental physics at the Collège de France in
1824. Was elected a member of the Royal Society in 1827. Was also a mumber of the