相关论文: Why do we use constants of motion while studying t…

A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the…

The rise of the top is studied by considering slipping friction. For this case, equations of motion are obtained by using Euler equations for a heavy symmetric top with a hemispherical peg. Different situations are considered to see how the…

Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one…

Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…

The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…

I discuss the precession motion of a symmetrical top without the assumption that its precessional velocity is much smaller than its spin angular velocity. I derive the general formula for the precessional velocity in an elementary way and…

This research investigates the rotational dynamics of a charged axisymmetric spinning rigid body influenced by gyrostatic torque. The study also accounts for the effects of transverse and constant body-fixed torques and an electromagnetic…

We investigate the consistency of the fundamental governing equations of motion in continuum mechanics. In the first step, we examine the governing equations for a system of particles, which can be considered as the discrete analog of the…

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the…

Small oscillations of a heavy symmetric top are studied when magnitudes of conserved angular momenta are equal to each other. Results show that the small oscillation approximation can be used in these cases.

In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…

Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…

Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…

We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…

In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the…

The dissipative motion and the rise of a heavy symmetrical top with a hemispherical peg are studied. A model taking the fixed point of the top as the center of the peg is considered when the top completely slips and the rolling motion is…

We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…

In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…

This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…

Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newton's third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall…