46 citations · 141 across the 27 of their papers we have counts for
27 papers
Generalized Lie Symmetries and Almost Regular Lagrangians: A Link Between Symmetry and Dynamics
Achilles D. Speliotopoulos
The generalized Lie symmetries of almost regular Lagrangians are studied, and their impact on the evolution of dynamical systems is determined. It is found that if the action has a…
Dark Energy and Extending the Geodesic Equations of Motion: A Spectrum of Galactic Rotation Curves
Achilles D. Speliotopoulos
A recently proposed extension of the geodesic equations of motion, where the worldline traced by a test particle now depends on the scalar curvature, is used to study the formation…
Constrained Dynamics: Generalized Lie Symmetries, Singular Lagrangians, and the Passage to Hamiltonian Mechanics
Achilles D. Speliotopoulos
Guided by the symmetries of the Euler-Lagrange equations of motion, a study of the constrained dynamics of singular Lagrangians is presented. We find that these equations of motion…
Volatilities That Change with Time: The Temporal Behavior of the Distribution of Stock-Market Prices
Achilles D. Speliotopoulos
While the use of volatilities is pervasive throughout finance, our ability to determine the instantaneous volatility of stocks is nascent. Here, we present a method for measuring t…
Dark Energy and Extending the Geodesic Equations of Motion: Its Construction and Experimental Constraints
Achilles D. Speliotopoulos
With the discovery of Dark Energy, , there is now a universal length scale, , associated with the universe that allows for an extension of the…
Dark Energy and Extending the Geodesic Equations of Motion: Connecting the Galactic and Cosmological Length Scales
Achilles D. Speliotopoulos
Recently, an extension of the geodesic equations of motion using the Dark Energy length scale was proposed. Here, we apply this extension to the analyzing the motion of test partic…