D. D. Holm
3
M3-4-5A34 Assessed Problems # 3
Due 15 Mar 2013
1
M3-4-5A16 Assessed Problems # 3:
Do all four problems
Exercise 3.1 (Momentum map for the Heisenberg group).
The Heisenberg group is a subgroup of
1
H = 0
0
SL(3, R) given by the upper triangul
Geometric Mechanics and Symmetry:
From Finite to Innite Dimensions
Darryl D. Holm
Imperial College London
Tanya Schmah
Macquarie University and The University of Toronto
Cristina Stoica
Wilfrid Laurier University
With solutions to selected exercises by Da
D. D. Holm
2
M3-4-5A34 Assessed Problems # 2
Due 1 Mar 2013
1
M3-4-5A16 Assessed Problems # 2:
Do all four problems
Exercise 2.1 (Adjoint and coadjoint actions for SE (2).
(A) Compute the the adjoint and coadjoint actions AD, Ad, ad, Ad and ad for SE (2).
D. D. Holm
1
M3-4-5A34 Assessed Problems # 1
Due 1 Feb 2013
1
M3-4-5A16 Assessed Problems # 1:
Do all three problems
Exercise 1.1 (Quaternions in Cayley-Klein (CK) parameters).
Express all of your answers for this exercise in terms of Cayley-Klein (CK) pa