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Published **1990**
by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, D.C, Springfield, Va .

Written in English

- Algorithms.,
- Iteration.,
- Lie groups.,
- Polynomials.,
- Trajectories.

**Edition Notes**

Statement | Matthew A. Grayson, Robert Grossman. |

Series | NASA contractor report -- NASA CR-187318. |

Contributions | Grossman, Robert, 1957-, United States. National Aeronautics and Space Administration. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15405688M |

Get this from a library! The simultaneous integration of many trajectories using nilpotent normal forms. [Matthew A Grayson; Robert Grossman; United . The simultaneous integration of many trajectories using nilpotent normal forms. is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. the main theorem; simultaneous integration of trajectories; and examples Topics Author: Robert Grossman and Matthew A. Grayson. These results are relevant for the analysis of local optimization problems, using high order nilpotent approximations. Keywords Vector Field Optimal Trajectory Linear Projection Iterate Integral Cited by: 4. Given two nilpotent matrix B1 and B2 over complex numbers which commute i.e. [B1,B2]=0, we know that they can be conjugated to upper-triangular ones (even strictly-triangular since they're nilpotent). But, can we conjugate them to upper-triangular ones so that one of them e.g. B1 gets into its Jordan normal form? Thanks for any help!

Sections take up nilpotent connections in characteristic j&>o. The notion of a nilpotent connection is due to Berthelot (cf. [i]). We would like to call attention to the beautiful formula () of Deligne. The main result () is that, in characteristic^, the Gauss-Manin connection on H^R(X/S) is nilpotent . The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then be used to construct explicit trajectories to drive the system between any two by: (the normalisation of) any nilpotent orbit, including non-Richardson orbits.2 We use this Nilpotent Orbit Normalisation (or \NON") formula to calculate normal nilpotent orbits of many Exceptional groups, although the high dimensions of their Weyl groups restrict . Of course we are using here the correspondence between (normal) subgroups of G=Z n and (normal) subgroups of G that contain Z n. The descending and ascending central series are closely related. PROPOSITION 7(i): Suppose G r Z n r. Then G r 1 Z n r+1. (For example, the hypothesis holds if G is nilpotent with G n = f1gand r = n. By decreasing.

If a Lie algebra g can be generated by M of its elements E1,, EM, and if any other Lie algebra generated by M other elements F1,, FM is a homomorphic image of g under the map Ei → Fi, we say that it is the free Lie algebra on M generators. The free nilpotent Lie algebra gM,r on M generators of rank r is the quotient of the free Lie algebra by the ideal gr+1 generated as. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to construct explicit trajectories to drive the system between any two points. A Technique to Compute Stable Manifolds in Noninvertible Discrete-time Dynamical Systems The simultaneous integration of many trajectories using nilpotent normal forms. simultaneous. Optimal Control on Nilpotent Lie Groups. at which we propose a new normal form that generalizes the canonical contact system on J n (ℝ,ℝ m) in a way analogous to that how Kumpera-Ruiz.

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