Programme

Lectures

• A) Geometric Mechanics and Control
  • Donghua Shi (Beijing Institute of Technology, China)
  • Dmitry Zenkov (North Carolina State University, USA)
• B) Introduction to Global Variational Geometry
  • Demeter Krupka (Beijing Institute of Technology, China; University of Ostrava, Czech Republic)

Contents

Dmitry Zenkov: Geometric Mechanics

There are two primary expositions of mechanics. Lagrangian mechanics concentrates on variational principles. Hamiltonian mechanics, while being variational too, focuses on such features as symplectic (more generally, Poisson) maps defined by systems' phase flow and canonical transformations. These two formalisms are often, but not always, equivalent. We will mostly confine our attention to Lagrangian mechanics, studying the classical variational principle as well as some of their contemporary developments. The tentative plan is to cover

• Newton's laws, Euler-Lagrange equations, and Hamilton's princile
• The rigid body and the Euler-Poincare equations
• Moving frames and Hamel's equations
• Variational principles for Hamel's equations
• Symmetry and conservation laws
• Systems with velocity constraints

Demeter Krupka: Introduction to Global Variational Geometry

The aim of the lectures is to give an introduction to advanced calculus of variations on smooth manifolds and to the research topics in this field. The following topics will be covered:

• Fundamentals of the variational theory on fibred manifolds. This part of the lectures is available on request in electronic form; the book was written as an introduction with broad coveridge of the subject, containing complete proofs (see the Contents below).
• Additional topics:
  - Variational sequences and applications, interior Euler-Lagrange operators, variational energy-momentum tensors,
  - Variational problems in parametric form, homogeneity and the inverse problem of the calculus of variations.

The following written text covering the school programme is available: download

Short presentations, Posters

A session of short presentations and posters is organized on Saturday and Sunday, in the afternoon. We plan to publish Extended Abstract Book of short presentations and posters. Please send your extended abstract to the organizers (jan.brajercik@unipo.sk) not later than 1 AUGUST 2012. Organizers recommend to prepare an abstract in LaTeX or MS Word (Example Abstract is available Here) with range of one B5 page (equations are allowed), including Key Words and MSC 2010.

Time Schedule

Thursday 16 August
Arrival

Friday 17 August:
9:00 Opening the Summer School
9:15–10:30 Lecture
11:00-12:30 Lecture
15:00 Levoča sigtseeing

Saturday 18 August
9:00-10:30 Lecture
11:00-12:30 Lecture
15:00-17:00 Presentations, Poster Session, Discussions

Sunday 19 August
9:00-10:30 Lecture
11:00-12:30 Lecture
15:00-17:00 Presentations, Poster Session, Discussions

Monday 20 August
Excursions

Tuesday 21 August
9:00-10:30 Lecture
11:00-12:30 Lecture
14:30-evening Farewell Party (barbecue)

Wednesday 22 August
9:00-10:30 Lecture
11:00-12:30 Lecture