3 edition of **The Herglotz lectures on contact transformations and Hamiltonian systems** found in the catalog.

The Herglotz lectures on contact transformations and Hamiltonian systems

Ronald B. Guenther

- 173 Want to read
- 13 Currently reading

Published
by Juliusz Schauder Center for Nonlinear Studies. Nicholas Copernicus University in Toruń [Poland] .

Written in English

- Contact transformations.,
- Hamiltonian systems.

**Edition Notes**

These are the completely reworked notes taken by professor Hans Schwerdtfeger as a student of Gustav Herglotz.

Statement | R.B. Guenther, C.M. Guenther, J.A. Gottsch. |

Series | Lecture notes in nonlinear analysis -- v. 1., Lecture notes in nonlinear analysis -- v. 1. |

Contributions | Schwerdtfeger, Hans., Herglotz, Gustav, 1881-, Guenther, C. M., Gottsch, J. A., Centrum im. Juliusza Schaudera (Toruń, Poland) |

The Physical Object | |
---|---|

Pagination | iv, 167 p. : |

Number of Pages | 167 |

ID Numbers | |

Open Library | OL15451114M |

ISBN 10 | 832310736X |

OCLC/WorldCa | 37340530 |

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The Herglotz lectures on contact transformations and Hamiltonian systems by Ronald B. Guenther; 1 edition; Subjects: Contact transformations, Hamiltonian systems. The Herglotz lectures on contact. and optimal control theories with contact transformations [5 for the Hamiltonian system of Herglotz type on.

The Herglotz Lectures on Contact Transformations and Hamiltonian Systems. Lecture Notes in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, Torún () Google Scholar by: In his lectures on “Berfihrungstransformationen” [Lecture Notes of the Juliusz Center for Nonlinear Studies, Guenther, Gottsch, and Guenther, Juliusz Center for Nonlinear Studies, ], Gustav Herglotz gave an algorithm for constructing canonical transformations.

We present Herglotz’s technique, which does not seem to be widely Cited by: The Herglotz algorithm for constructing autonomous canonical transformations that was presented by Guenther, Gottsch, and Kramer in [SIAM Rev., 38 (), pp. ] is extended to include nonautonomous canonical transformations and a remainder function ${\cal R}^*$ that is related to a generating function by ${\cal R}^* = \partial F/\partial t$.Cited by: 5.

Guenther, A. Gottsch, and C. Guenther, The Herglotz Lectures on Contact Transformations and Hamiltonian Systems (Juliusz Center for Nonlinear Studies, ). Guenther, A. Gottsch, and C. Guenther, The Herglotz Lectures on Contact Transformations and Hamiltonian Systems (Juliusz Center for Nonlinear Studies, ).

Google Scholar 4. Guenther and J. Gottsch, “ The Herglotz lectures on contact transformations and Hamiltonian systems,” in Lecture Notes in Nonlinear Analysis (Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, Torún, ), Vol.

The Herglotz Lectures on Contact Transformations and Hamiltonian Systems; Juliusz Center for Nonlinear Studies: Torun, Poland, Georgieva, B.; Guenther, R. First, Noether-type theorem for the generalized variational principle of Herglotz.

Topol. Methods Nonlinear Anal. Canonical Transformations, Hamilton-Jacobi Equations, and Action-Angle Variables We’ve made good use of the Lagrangian formalism. Here we’ll study dynamics with the Hamiltonian formalism.

Problems can be greatly simpli ed by a good choice of generalized coordinates. How far can we push this.

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The Herglotz Lectures on Contact Transformations and Hamiltonian Systems. Schauder Center For Nonlinear Studies, Copernicus University () Google Scholar The Herglotz Lectures on Contact Transformations and Hamiltonian Systems.

Juliusz Center for Nonlinear Studies, Torun, Poland, Lectures at the University of Gottingen. Abstract Herglotz proposed a generalized variational principle through his work on contact transformations and their connections with Hamiltonian systems and Poisson brackets, which provides an effective method to study the dynamics of nonconservative systems.

The Herglotz Lectures on Contact Transformations and Hamiltonian Systems. Lecture Notes in Nonlinear Analysis, vol. Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, Torún (). The variational theories for more general contact Hamiltonian systems with arbitrary degree The Herglotz lectures on contact transformations and Hamiltonian systems still unpublished book.

Guenther, C. Guenther, and J. Gottsch, The Herglotz Lectures on Contact Transformations and Hamiltonian Systems, Juliusz Center for Nonlinear Studies (Copernicus University, ).

Google Scholar 7. Guenther, H. Schwerdtfeger, G. Herglotz, C. Guenther and J. Gottsch, The Herglotz lectures on contact transformations and Hamiltonian systems, in Juliusz Schauder Center for Nonlinear Studies (Nicholas Copernicus University, ).

Guenther RB, Guenther CM, Gottsch JA () The Herglotz lectures on contact transformations and hamiltonian systems, vol 1. Lecture notes in nonlinear analysis. Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, TorúnGoogle Scholar R.

Guenther, J. Gottsch and C. Guenther, The Herglotz Lectures on Contact Transformations and Hamiltonian Systems, Juliusz Center for Nonlinear Studies, \plr Toruä () \ref\key 8. canonical transformations, SIAM Rev.

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Lecture 1: Hamiltonian systems Table of contents 1 Derivation from Lagrange’s equation 1 2 Energy conservation and ﬁrst integrals, examples 3 3 Symplectic transformations 5 4 Theorem of Poincare´ 7 5 Generating functions 9 6 Hamilton–Jacobi partial differential equation 11 7 Exercises Infinitesimal symmetries for a contact Hamiltonian system.

Next, we will introduce a class of infinitesimal symmetries for a contact Hamiltonian system (M, η, H) which will be very useful on the next section. First we prove the following result, which help us to.

Guenther, C. Guenther and J. Gottsch, The Herglotz Lectures on Contact Transformations and Hamiltonian Systems Lecture Notes in Nonlinear Analysis, Vol. 1, Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, Torún, Don't show me this again. Welcome.

This is one of over 2, courses on OCW. Find materials for this course in the pages linked along the left. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. No enrollment or registration. For the time-delayed Hamiltonian system of Herglotz type, if the infinitesimal transformations of group are the Noether symmetric transformations of the system, then the system exists with r linear independent conserved quantities as follows (60) I σ = λ t p s t ξ s σ − H t ξ 0 σ + λ t + τ p s τ t + τ ξ s σ = C σ, t ∈ t 0, t 1.

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Nicholas Copernicus University, Google Scholar [16]. X. Tian, Y. ZhangNoether symmetry and conserved quantity for Hamiltonian system of Herglotz type on time scales Acta Mech (), /s Google Scholar. The Herglotz Lectures on Contact Trans- formations and Hamiltonian Systems, Lecture Notes in Nonlinear Analysis, Vol.

1, Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, Toru´n, (). In this paper, we discuss the singular Lagrangian systems on the framework of contact geometry.

These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic one studied by Gotay and Nester (the geometrization of the well-known Dirac–Bergmann algorithm).

Another remarkable similarity with standard symplectic Hamiltonian systems is the fact that contact Hamiltonian systems have an associated variational principle, which is due to Herglotz [25, 34] (see also [13, 55]), and a corresponding theory of generating functions [].Geometric integrators for contact Hamiltonian systems have been studied in [] by exploiting their symplectification and the.

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2 (), no. 3, ]. E. Whittaker explained what a contact transformation is in the book "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies". This was an apparently important book for Dirac and it develops the basis for Canonical Quantization - Poisson Brackets wherein a contact transformation is involved.

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New exercises and new sections in canonical transformation and Hamiltonian theory have been added. Tian X., Zhang r symmetry and conserved quantity for Hamiltonian system of Herglotz type on time scales Acta Mech., (), pp.

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