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Regularization of damped motion under central forces in two and three-dimensions are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in $frac{1}{r}$ potential and subjected to a damping force is shown to be regularized a la Levi-Civita. We then generalize this regularization mapping to the case of damped motion in the potential $r^{-frac{2N}{N+1}}$. Further equation of motion of a damped Kepler motion in 3-dimensions is mapped to an oscillator with inverted sextic potential and couplings, in 4-dimensions using Kustaanheimo-Stiefel regularization method. It is shown that the strength of the sextic potential is given by the damping co-efficient of the Kepler motion. Using homogeneous Hamiltonian formalism, we establish the mapping between the Hamiltonian of these two models. Both in 2 and 3-dimensions, we show that the regularized equation is non-linear, in contrast to undamped cases. Mapping of a particle moving in a harmonic potential subjected to damping to an undamped system with shifted frequency is then derived using Bohlin-Sudman transformation.
Two damped, central force systems are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in $frac{1}{r}$ potential and subjected to a damping force is shown to be regularized a la Levi-Civita. This mapping i
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number
We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, and we apply it to prove the Kac conjecture for hard sphere collision in three dimensions.
We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex Monge-Ampere equation. The lift is applied to noninvariant sol
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