Classical Variational Problems

Part of the Texts and Monographs in Physics book series (TMP)


In many applications of the calculus of variations we have specific information about the form of the functional f which we want to minimise. In practical terms, this means that the functional f has the form
$$f(\varphi ) = \int_I {F(t,\varphi (t),\varphi '(t), \ldots ,{\varphi ^{(n)}}(t))} dt,{\varphi ^{(p)}}(t) = \frac{{{d^p}\varphi }}{{d{t^p}}}(t),$$
where we have a certain function \(F:I \times {\mathbb{R}^{N + 1}} \to \mathbb{R},\varphi :I \to \mathbb{R},\) and a compact interval I= [a, b] or, alternatively, an equivalent generalisation to functions φ of several variables and to functions φ with values in ℝ p , p>1.


Banach Space Euler Equation Lagrangian Density Jacobi Equation Classical Mechanics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Theoretische Physik, Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa

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