| Title:
|
Algebraic integrability for minimum energy curves (English) |
| Author:
|
Yudin, Ivan |
| Author:
|
Silva Leite, Fátima |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
321-334 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed. (English) |
| Keyword:
|
Darboux polynomials |
| Keyword:
|
drag power |
| Keyword:
|
Euler–Lagrange equations |
| Keyword:
|
grading |
| Keyword:
|
integrability |
| Keyword:
|
vector fields |
| MSC:
|
13N15 |
| MSC:
|
34A34 |
| MSC:
|
34C07 |
| MSC:
|
34C14 |
| MSC:
|
34H05 |
| idZBL:
|
Zbl 06487082 |
| idMR:
|
MR3350565 |
| DOI:
|
10.14736/kyb-2015-2-0321 |
| . |
| Date available:
|
2015-06-19T15:25:43Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144301 |
| . |
| Reference:
|
[1] Crouch, P., Leite, F. Silva: The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces..J. Dynam. Control Systems 1 (1995), 2, 177-202. MR 1333770, 10.1007/bf02254638 |
| Reference:
|
[2] Camarinha, M., Leite, F. Silva, Crouch, P.: On the geometry of Riemannian cubic polynomials..Differential Geom. Appl. 15 (2001), 15, 107-135. MR 1857558, 10.1016/s0926-2245(01)00054-7 |
| Reference:
|
[3] Goriely, A.: Integrability and Nonintegrability of Dynamical Systems..Advanced Series in Nonlinear Dynamics 19, World Scientific Publishing Co., Inc., River Edge, NJ 2001. Zbl 1002.34001, MR 1857742, 10.1142/9789812811943 |
| Reference:
|
[4] Hartman, P.: Ordinary Differential Equations..John Wiley and Sons Inc., New York 1964. Zbl 1009.34001, MR 0171038 |
| Reference:
|
[5] Häusler, A. J., Saccon, A., Aguiar, A. P., Hauser, J., Pascoal, A.: Cooperative motion planning for multiple autonomous marine vehicles..In: Proc. 9th IFAC Conference on Manoeuvring and Control of Marine Craft 2012 (G. Bruzzone, ed.), International Federation of Automatic Control, 2012, pp. 244-249. 10.3182/20120919-3-it-2046.00042 |
| Reference:
|
[6] Kruger, D., Stolkin, R., Blum, A., Briganti, J.: Optimal AUV path planning for extended missions in complex, fast-flowing estuarine environments..In: ICRA'07, IEEE 2007, pp. 4265-4270. 10.1109/robot.2007.364135 |
| Reference:
|
[7] Noakes, L., Heinzinger, G., Paden, B.: Cubic splines on curved spaces..IMA J. Math. Control Inform. 6 (1989), 4, 465-473. Zbl 0698.58018, MR 1036158, 10.1093/imamci/6.4.465 |
| . |
