## Abstract The 17^th^ century is considered as the cradle of modern natural sciences and technology as well as the begin of the age of enlightenment with the invention of analytical geometry by R. Descartes (1637), infinitesimal calculus by I. Newton (1668) and G. W. Leibniz (1674), and based on t
A Decoupling Principle in the Calculus of Variations
โ Scribed by F.H. Clarke
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 402 KB
- Volume
- 172
- Category
- Article
- ISSN
- 0022-247X
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๐ SIMILAR VOLUMES
We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.
The book by Bolza, in fact, became so popular that the fixed-endpoint problem we stated became known as the article no. 0162
## Communicated by G. F. Roach A numerical technique for determining the solution of the brachistochrone problem is presented. The brachistochrone problem is first formulated as a non-linear optimal control problem. Using Chebyshev nodes, we construct the Mth degree polynomial interpolation to ap
The purpose of this paper is to calculate the first variation of capacity and of the lowest eigenvalue for the Dirichlet problem in convex domains in R N . These formulas are well known in the smooth case and are due to Poincare and Hadamard, respectively. The point is to prove them in sufficient ge
Calculus of Variations: Fundamentals ### 9.1 Historical Background The calculus of variations was first found in the late 17th century soon after calculus was invented. The main figures involved are Newton, the two Bernoulli brothers, Euler, Lagrange, Legendre, and Jacobi. Isaac Newton (1642-1727