8 research outputs found
Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry
How does one measure the gravitational field? We give explicit answers to
this fundamental question and show how all components of the curvature tensor,
which represents the gravitational field in Einstein's theory of General
Relativity, can be obtained by means of two different methods. The first method
relies on the measuring the accelerations of a suitably prepared set of test
bodies relative to the observer. The second methods utilizes a set of suitably
prepared clocks. The methods discussed here form the basis of relativistic
(clock) gradiometry and are of direct operational relevance for applications in
geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D.
Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52
pages, in print. arXiv admin note: text overlap with arXiv:1804.11106,
arXiv:1511.08465, arXiv:1805.1067
Realization of nonlinear composite systems
The paper studies the realization problem for series and parallel connections of nonlinear single-input single-output systems, described by higher order differential equations. Necessary and sufficient conditions are given for the existence of the classical state space realization in both cases. It is proved that post- and parallel compensators are of no help in overcoming non-realizability. Results are illustrated by an example