High resolution analysis of satellite gradiometry

Satellite gravity gradiometry is a technique now under development which, by the middle of the next decade, may be used for the high resolution charting from space of the gravity field of the earth and, afterwards, of other planets. Some data analysis schemes are reviewed for getting detailed gravity maps from gradiometry on both a global and a local basis. It also presents estimates of the likely accuracies of such maps, in terms of normalized spherical harmonics expansions, both using gradiometry alone and in combination with data from a Global Positioning System (GPS) receiver carried on the same spacecraft. It compares these accuracies with those of current and future maps obtained from other data (conventional tracking, satellite-satellite tracking, etc.), and also with the spectra of various signals of geophysical interest

Quasivelocities and Optimal Control for Underactuated Mechanical Systems

This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system subjected to constraints. The equations of motion are geometrically derived using an adaptation of the classical Skinner and Rusk formalism.Comment: 8 page

Nonlinear elasticity of monolayer graphene

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior of one-atom thick carbon sheets and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.Comment: 4 page

Gravitational spectra from direct measurements

A simple rapid method is described for determining the spectrum of a surface field from harmonic analysis of direct measurements along great circle arcs. The method is shown to give excellent overall trends to very high degree from even a few short arcs of satellite data. Three examples are taken with perfect measurements of satellite tracking over a planet made up of hundreds of point-masses using (1) altimetric heights from a low orbiting spacecraft, (2) velocity residuals between a low and a high satellite in circular orbits, and (3) range-rate data between a station at infinity and a satellite in highly eccentric orbit. In particular, the smoothed spectrum of the Earth's gravitational field is determined to about degree 400(50 km half wavelength) from 1 D x 1 D gravimetry and the equivalent of 11 revolutions of Geos 3 and Skylab altimetry. This measurement shows there is about 46 cm of geoid height remaining in the field beyond degree 180