Report of Meeting for the Purpose of Obtaining the Views of the Three Affiliated Tribes of the Fort Berthold Reservation on the Lieu Lands Offered by the Secretary of War, 1946

Notice of meeting in the Secretary\u27s conference room to obtain the views of the Three Affiliated Tribes of the Fort Berthold Reservation of the lieu lands offered by the Secretary of War. Provides a copy of the transcript for the meeting and the exhibits explained during the meeting. Includes: Section 6 Public Law 374, 79th Congress 2d session, memorandum to Secretary of the interior from the acting commissioner of Indian Affairs on subject of Transmitting correspondence to Secretary, Letter from Chairman George Gillette accepting invitation to have representatives of the Three Affiliated Tribes at a special hearing. Also includes: notice to all members of the Three Affiliated Tribes of the Fort Berthold Reservation listing a schedule of meetings to be held to discuss offer and inform tribe of schedule; list of attendees and comments for meeting in Lucky Mound District on December 5, 1946; list of attendees and comments in Red Butte District on December 5, 1946; List of attendees and comments in Charging Eagle District on December 6, 1946; List of attendees and comments in Independence District on December 7, 1946; List of attendees and comments in Nishu District on December 8, 1946; List of attendees and comments in Shell Creek District on December 9, 1946; Resolution announcing rejection to offer for the lieu lands offered to the Three Affiliated Tribes; and Exhibit 4 - formal rejection of offer, and Exhibit 5 - letter from J.A. Krug, Secretary of the Intererior) warranted a restudy of the lands. See also: Report of Second Meeting for the Purpose of Obtaining the Views of the Three Affiliated Tribes of the Fort Berthold Reservation on the Lieu Lands Offered by the Secretary of War, 1946https://commons.und.edu/langer-papers/1144/thumbnail.jp

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

Probing rare physical trajectories with Lyapunov weighted dynamics

The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition, atypical structures like the first chaotic regions to appear, or the last regular islands to survive, play a crucial role in many physical situations. For instance, resonances and separatrices determine the fate of planetary systems, and localised objects like solitons and breathers provide mechanisms of energy transport in nonlinear systems such as Bose-Einstein condensates and biological molecules. Unfortunately, despite the fundamental progress made in the last years, most of the numerical methods to locate these 'rare' trajectories are confined to low-dimensional or toy models, while the realms of statistical physics, chemical reactions, or astronomy are still hard to reach. Here we implement an efficient method that allows one to work in higher dimensions by selecting trajectories with unusual chaoticity. As an example, we study the Fermi-Pasta-Ulam nonlinear chain in equilibrium and show that the algorithm rapidly singles out the soliton solutions when searching for trajectories with low level of chaoticity, and chaotic-breathers in the opposite situation. We expect the scheme to have natural applications in celestial mechanics and turbulence, where it can readily be combined with existing numerical methodsComment: Accepted for publication in Nature Physics. Due to size restrictions, the figures are not of high qualit

Relativistic Celestial Mechanics with PPN Parameters

Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.Comment: 71 page