466 research outputs found
Doubly Special Relativity and Finsler geometry
We discuss the recent proposal of implementing Doubly Special Relativity in
configuration space by means of Finsler geometry. Although this formalism leads
to a consistent description of the dynamics of a particle, it does not seem to
give a complete description of the physics. In particular, the Finsler line
element is not invariant under the deformed Lorentz transformations of Doubly
Special Relativity. We study in detail some simple applications of the
formalism.Comment: 8 pages, plain Te
Interplanetary Transfer Trajectories Using the Invariant Manifolds of Halo Orbits
Throughout the history of interplanetary space travel, the Newtonian dynamics of the two-body problem have been used to design orbital trajectories to traverse the solar system. That is, that a spacecraft orbits only one large celestial body at a time. These dynamics have produced impressive interplanetary trajectories utilizing numerous gravity assists, such as those of Voyager, Cassini, Rosetta and countless others. But these missions required large amounts of delta-v for their maneuvers and therefore large amounts of fuel mass. As we desire to travel farther and more extensively in space, these two-body dynamics lead to impossibly high delta-v values, and missions become infeasible due to the massive amounts of fuel that they would need to carry. In the last few decades a new dynamical system has been researched in order to find new ways of designing mission trajectories: the N-body problem. This utilizes the gravitational acceleration from multiple celestial bodies on a spacecraft, and can lead to unconventional, but very useful trajectories.
The goal of this thesis is to use the dynamics of the Circular Restricted Three-Body Problem (CRTBP) to design interplanetary transfer trajectories. This method of modelling orbital dynamics takes into account the gravitational acceleration of two celestial bodies acting on a spacecraft, rather than just one. The invariant manifolds of halo orbits about Sun-planet Lagrange points are used to aid in the transfer from one planet to another, and can lead into orbital insertion about the destination planet or flyby trajectories to get to another planet. This work uses this method of dynamics to test transfers from Earth to both Jupiter and Saturn, and compares delta-v and time of flight values to traditional transfer methods. Using the CRTBP can lead to reduced delta-v amounts for completing the same missions as two-body dynamics would. The aim of this work is to research if using manifolds for interplanetary transfers could be superior for some high delta-v missions, as it could drastically reduce the required delta-v for maneuvers. With this method it could be possible to visit more distant destinations, or carry more mass of scientific payloads, due to the reduced fuel requirements.
Results of this research showed that using manifolds to aid in interplanetary transfers can reduce the delta-v of both departure from Earth and arrival at a destination planet. For transfers to Jupiter the delta-v for the interplanetary transfer was reduced by 4.12 km/s compared to starting and ending in orbits about the planets. For a transfer to Saturn the delta-v required for the interplanetary transfer was reduced by 6.77 km/s. These delta-v savings are significant and show that utilizing manifolds can lead to lower energy interplanetary transfer trajectories, and have the potential to be useful for high delta-v missions
Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators
We construct invariant differential operators acting on sections of vector
bundles of densities over a smooth manifold without using a Riemannian metric.
The spectral invariants of such operators are invariant under both the
diffeomorphisms and the gauge transformations and can be used to induce a new
theory of gravitation. It can be viewed as a matrix generalization of Einstein
general relativity that reproduces the standard Einstein theory in the weak
deformation limit. Relations with various mathematical constructions such as
Finsler geometry and Hodge-de Rham theory are discussed.Comment: Version accepted by J. High Energy Phys. Introduction and Discussion
significantly expanded. References added and updated. (41 pages, LaTeX: JHEP3
class, no figures
An Expansion Term In Hamilton's Equations
For any given spacetime the choice of time coordinate is undetermined. A
particular choice is the absolute time associated with a preferred vector
field. Using the absolute time Hamilton's equations are
+ (\delta H_{c})/(\delta \pi)=\dot{q}\Theta = V^{a}_{.;a}N\equiv exp(-\int\Theta d \ta)\pi^{N}\pi^N$. Briefly the possibility of a non-standard sympletic form
and the further possibility of there being a non-zero Finsler curvature
corresponding to this are looked at.Comment: 10 page
Multi-transmission-line-beam interactive system
We construct here a Lagrangian field formulation for a system consisting of
an electron beam interacting with a slow-wave structure modeled by a possibly
non-uniform multiple transmission line (MTL). In the case of a single line we
recover the linear model of a traveling wave tube (TWT) due to J.R. Pierce.
Since a properly chosen MTL can approximate a real waveguide structure with any
desired accuracy, the proposed model can be used in particular for design
optimization. Furthermore, the Lagrangian formulation provides for: (i) a clear
identification of the mathematical source of amplification, (ii) exact
expressions for the conserved energy and its flux distributions obtained from
the Noether theorem. In the case of uniform MTLs we carry out an exhaustive
analysis of eigenmodes and find sharp conditions on the parameters of the
system to provide for amplifying regimes
The Dirac-Nambu-Goto p-Branes as Particular Solutions to a Generalized, Unconstrained Theory
The theory of the usual, constrained p-branes is embedded into a larger
theory in which there is no constraints. In the latter theory the
Fock-Schwinger proper time formalism is extended from point-particles to
membranes of arbitrary dimension. For this purpose the tensor calculus in the
infinite dimensional membrane space M is developed and an action which is
covariant under reparametrizations in M is proposed. The canonical and
Hamiltonian formalism is elaborated in detail. The quantization appears to be
straightforward and elegant. No problem with unitarity arises. The conventional
p-brane states are particular stationary solutions to the functional
Schroedinger equation which describes the evolution of a membrane's state with
respect to the invariant evolution parameter tau. A tau-dependent solution
which corresponds to the wave packet of a null p-brane is found. It is also
shown that states of a lower dimensional membrane can be considered as
particular states of a higher dimensional membrane.Comment: 28 page
Invariant and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants,
determinants, characteristic polynomials and polynomial identities for matrices
of higher rank. We define permutation tensors and in term of them we construct
discriminants and the determinant as the discriminant of order , where
is the dimension of the matrix. The characteristic polynomials and the
Cayley--Hamilton theorem for higher rank matrices are obtained there from
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
Prospectus, April 9, 1983
WELCOME SPRING!; News Digest; Job fair figures show rosy future for some; PC donors can aid Miller; Editor accused of bias; PC jazz groups perform at UI; GM seminar offers new regional training; Animals suffer for science; Judges deliberating; Readers look to the stars for favorite feature: Question: What is your favorite Prospectus feature?; Instructor prefers teaching to testing; Club Notes; C-U happenings; Signs of Spring...; Classified; Skylines; Trivia quiz; Selleck adventure surprisingly good; Sport shortshttps://spark.parkland.edu/prospectus_1983/1020/thumbnail.jp
Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
A generalized model of space-time is given, taking into consideration the
anisotropic structure of fields which are depended on the position and the
direction (velocity).In this framework a generalized FRW-metric the
Raychaudhouri and Friedmann equations are studied.A long range vector field of
cosmological origin is considered in relation to the physical geometry of
space-time in which Cartan connection has a fundamental role.The generalised
Friedmann equations are produced including anisotropic terms.The variation of
anisotropy is expressed in terms of the Cartan torsion tensor of the
Finslerian space-time.A possible estimation of the anisotropic parameter
can be achieved with the aid of the de-Sitter model of the empty flat universe
with weak anisotropy. Finally a physical generalisation for the model of
inflation is also studied.Comment: 21 pages- to appear in GR
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