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301.023 Hamiltonian Systems
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2022S, SV, 2.0h, 3.0EC


  • Semester hours: 2.0
  • Credits: 3.0
  • Type: SV Special Lecture
  • Format: Online

Learning outcomes

After successful completion of the course, students are able to derive Hamiltonian equations of motion and to apply analytical methods (Normal Forms, generating functions) to simplify the equations and determine special solutions.

Subject of course

Solution methods for Hamiltonian Systems are introduced and demonstrated for selected examples. 1.) Motivation: Mechanical systems, Maximum principle in optimal control; 2.) Inntroduction: Simple modells; 3.) Linear Equations, Symplectic transformations; 4.) Hamiltonian systems with symmetry, conservation laws, Energy-momentum map. 5.) Birkhoff's Normal Form, resonances; 6.) Perturbation Theory, Averaging method; 7.) Numerical integration.

Teaching methods

Discussion and treatment of model examples.

Mode of examination

Written and oral

Additional information

Anwendungen in Mechanik und Op.Research



Course dates

Wed08:30 - 10:0002.03.2022 - 29.06.2022 Abhaltung über ZoomsitzungVorlesung
Tue08:00 - 10:0015.03.2022 - 28.06.2022Seminarraum BA 02C Vorlesung
Hamiltonian Systems - Single appointments
Wed02.03.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Wed09.03.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue15.03.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed16.03.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue22.03.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed23.03.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue29.03.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed30.03.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue05.04.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed06.04.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue26.04.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed27.04.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue03.05.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed04.05.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue10.05.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed11.05.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue17.05.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed18.05.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung
Tue24.05.202208:00 - 10:00Seminarraum BA 02C Vorlesung
Wed25.05.202208:30 - 10:00 Abhaltung über ZoomsitzungVorlesung

Examination modalities

Treatment of a model example.

Course registration

Begin End Deregistration end
23.02.2022 12:00

Registration modalities

Anmeldung in TISS


Study CodeObligationSemesterPrecon.Info
033 201 Technical Mathematics Mandatory elective
066 445 Mechanical Engineering Elective
066 482 Mechanical Engineering - Management Elective
700 Mechanical Engineering Mandatory elective


Lecture notes for this course are available. Wird ausgeteilt.

Previous knowledge

Ordinary differential equations, Mechanics (Hamiltonian and Lagrangian equations), Optimal control.