Introduction to Geometric Mechanics and Differential Geometry


Dates Topic Supporting Math Concept Book Section Homework Notes
29-Aug Joints/Links, configuration space, intro to velocity Direct product, isomorphism (homeomorphisms),diffeomorphism, manifold, groups, Lie group,  tangent spaces, vector fields 1.1-1.2, 1.4   Howie
31-Aug Rigid bodies in SE(2) Semi-direct products,  linear algebra ( vector algebra, matrix anxiety, null spaces, index notation?) 1.2-1.4   Howie
5-Sep Labor Day       No class
7-Sep SE(2) velocities, spatial and body velocities  lifted actions, lifted action examples, geodesics 1.5   Howie
12-Sep SE(2) velocities adjoint and exponential map 1.6   Ross
14-Sep Finish chapter 1 day frames, notation 1 HW1 Assigned Ross
19-Sep Articulated sytems, fixed base systems (new ross notation), proximal vs. medial vs. distal, start mobile articulated systems holonomic constraints 2.1-2.2   Howie
21-Sep mobile articulated systems, generalized body frames   2.3-2.4   Ross
26-Sep IROS       No class
28-Sep IROS       No class
3-Oct Jacobians Review adjoints 2.5   Howie
5-Oct Jacobian examples   2.5 HW 1 Due      HW 2 Assigned Howie
10-Oct Kinematic Locomotion up to differential car - Pfaffian constraints and Connection, connection vectorfields directional linearity, linearity, nonholonomic constraints 3.1-3.3 HW1-A,B Howie
12-Oct Connection vectorfields, no-slide and inertial constraints locomotion one-forms, co-vectors, Noether's Theorem 3.4 HW1-C Howie
17-Oct Connection vectorfields, no-slide and inertial constraints locomotion Noether's Theorem revisited 3.4 HW1-D Howie
19-Oct Locomotion in fluids   3.4 HW1-E Ross?
24-Oct Gaits Basic definition of non-communitive and non conservative effects, Lie bracket, curl and Stokes Theorem HW 2 Due     HW 3 Assigned Howie
26-Oct Gaits - unify concepts review one-forms, two forms, reexplain curl, Lie brackets, and Stokes theorem again HW 2-A,B Howie
31-Oct Ross Code     HW 2-C,D Howie
2-Nov Chap 3 and 4 Review     HW 3 DUE    Assign HW 4 (code) Howie
7-Nov Murray and Walsh Papers       Students
19-Nov Coordinate Optimization Hodge-Helmoltz Decomposition 5 Re-assign HW 4 Howie
14-Nov Hatton (swim) and Meli Papers       Students
16-Nov Gait efficiency Distance metrics, geodesics, curvature 5   Howie
21-Nov Pre-thanksgiving       No class
23-Nov Pre-Thanksgiving       No class
28-Nov Kelly Paper     HW 4 due Students
30-Nov Finish Chap 5, Begin Mode Shapes       Ross
5-Dec TBD        
7-Dec TBD