Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.

Subparsec-scale structure and evolution of Centaurus A (NGC5128).

We present a series of 8.4-GHz very-long-baseline radio interferometry images of the nucleus of Centaurus A (NGC5128) made with a Southern Hemisphere array, representing a 3.3-year monitoring effort. The nuclear radio jet is approximately 50 milliarcseconds in extent, or at the 3.5-megaparsec distance of NGC5128, approximately 1 parsec in length. Subluminal motion is seen and structural changes are observed on time scales shorter than 4 months. High-resolution observations at 4.8 and 8.4 GHz made in November 1992 reveal a complex morphology and allow us to unambiguously identify the self-absorbed core located at the southwestern end of the jet.

The works, moral and religious, of Sir Matthew Hale, knt. ...

Mode of access: Internet.

The naval history of Great Britain, from the declaration of war by France in 1793 to the accession of George IV /

Mode of access: Internet.

The public health manual containing the Public Health law, the Sanitary code,and extracts from other state laws relating to public health. February 1, 1923.

At head of title: New York State Department of Health. Hermann M. Biggs, M.D., Commissioner.

Essays on the sources of the pleasures received from literary compositions.

Published anonymously; here ascribed to Greenfield, assistant professor of rhetoric at Edinburgh, 1784-1801, on authority of Grant, Story of Univ. of Edinb., 1884, v. 2, pt. 359; Scott, Fasti eccl. scot., v.1 (1915) p. 60-61; Notes & queries, 4 ser., v. 8, p. 75. In the Brit. mus. Catalogue, Dict. nat. biog., Green, Bibl. Somerset, and Halkett & Laing, Dict. of anon. and pseud. lit., it is ascribed to Edward Mangin. Cushing (Anonyms, 1889) attributes it to Martin MacDermot.

Mittheilungen aus dem Leben des französischen Oberstlieutenants Carl Christian Ludewig Schenck : enthaltend die Geschichte seiner Gefangennahme in der Schlacht bey Borodino in Russland am 7ten September 1812 ... /

Spine title: Oberst. Schenck, 1812-1814.

A treatise of the laws for the relief and settlement of the poor /

Includes index.

The new court.

Goldsmiths'-Kress no. 24743.

The sphere for joint-stock companies; or, The way to increase the value of land, capital, and labour : with an account of the establishment at Orbiston, in Lanarkshire /

Mode of access: Internet.

Observations on the old and new views, and their effects on the conduct of individuals : as manifested in the proceedings of the Edinburgh Christian Instructor and Mr. Owen /

Mode of access: Internet.

The religious creed of the new system : with an explanatory catechism, and an appeal in favour of true religion, to the ministers of all other religious persuasions and denomination /

Goldsmiths'-Kress no. 24355.

Afiḳe Yehudah : ...ha-derushim.

Mode of access: Internet.

Œuvres completes de Voltaire.

The plates by J.M. Moreau, originally intended to be kept and sold separately with an engraved t.-p. especially designed for them, are distributed in L.C. copy. The special t.-p. is wanting.