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We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
The effect of the frame dragging on the equation of motions, depends on the approaches that have been considered. Accordingly, additional force terms may appear or disappear. To understand the effect of radial and non-radial perturbations…
Relativistic addition of velocities in one dimension, though a mainstay of introductory physics, contributes much less physical insight than it could. For such calculations, we propose the use of velocity factors (two-way doppler factors).…
Physics students now have access to interactive molecular dynamics simulations that can model and animate the motions of hundreds of particles, such as noble gas atoms, that attract each other weakly at short distances but repel strongly…
We study the gravity assist in the general case, i.e. when the spacecraft is not in a coplanar motion with respect to the planet's orbit. Our derivation is based on Kepler's planetary motion and Galilean addition of velocities, subjects…
When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This…
This is a short introduction of the exterior form formalism focus on its applications in physics and then mostly aimed to physics students. As a rule of a game played here we never use a coordinate frame neither in the definitions nor in…
Objects that move in response to the actions of a main character often make an important contribution to the visual richness of an animated scene. We use the term "secondary motion" to refer to passive motions generated in response to the…
Obstacle avoidance for DMPs is still a challenging problem. In our previous work, we proposed a framework for obstacle avoidance based on superquadric potential functions to represent volumes. In this work, we extend our previous work to…
In computational 3D geometric problems involving rotations, it is often that people have to convert back and forth between a rotational matrix and a rotation described by an axis and a corresponding angle. For this purpose, Rodrigues'…
In dynamic environments, learned controllers are supposed to take motion into account when selecting the action to be taken. However, in existing reinforcement learning works motion is rarely treated explicitly; it is rather assumed that…
In my doctoral thesis, I have focussed my attention on radiation processes in high-energy astrophysics connected with the accretion flow physics around compact objects. Generally, a radiation field beside to exert an outward radiation…
This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear…
For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…
The long-term dynamics of perturbed Keplerian motion is usually analyzed in simplified models as part of the preliminary design of artificial satellites missions. It is commonly approached by averaging procedures that deal with literal…
We are interested in the naive problem whether we can move a solid object in a solid box or not. We restrict move to rotation. In the case we can, the centre and the ``direction'' of rotation may be restricted. Simplifying, we consider…
We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
We develop a fully relativistic framework to study the rotational response of gravitationally coupled two-fluid neutron stars within the slow-rotation approximation. Treating the two components as independently conserved perfect fluids…