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arXiv · 2609.08028

New Symbolic Procedures in the Study of Dynamical Systems

Daniel Condurache
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Abstract

The thesis develops symbolic representations of dynamical systems in finite-dimensional commutative real algebras. The algebraic framework (orthogonal idempotents, zero divisors, and the structure of finite-order algebras) supports algebra-valued Fourier and Laplace transforms and Walsh-function-based system identification. The methods yield exact, coordinate-free vectorial solutions for motion in non-inertial reference frames, including a generalized Larmor theorem, the Foucault pendulum, motion in central positional-force fields, and the two-body problem in arbitrarily rotating reference frames. This English edition is an audited LaTeX reconstruction of the 1995 original, with an editorial note documenting provenance.

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Daniel Condurache. 2026-09-07. New Symbolic Procedures in the Study of Dynamical Systems. https://arxiv.org/abs/2609.08028

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