Related papers: Twisting Somersault
We present and analyse a simple model for the twisting somersault. The model is a rigid body with a rotor attached which can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining…
We present the mathematical framework of an athlete modelled as a system of coupled rigid bodies to simulate platform and springboard diving. Euler's equations of motion are generalised to non-rigid bodies, and are then used to innovate a…
We derive the equations of motion for the planar somersault, which consist of two additive terms. The first is the dynamic phase that is proportional to the angular momentum, and the second is the geometric phase that is independent of…
We study the motion of self deforming bodies with non zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame,…
The motion of a rigid body is described in Classical Mechanics with the venerable Euler's equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however,…
Euler's rotation theorem states that any reconfiguration of a rigid body with one of its points fixed is equivalent to a single rotation about an axis passing through the fixed point. The theorem forms the basis for Chasles' theorem which…
Whenever a freely spinning body is found in a complex rotational state, this means that either the body is a recent victim of an impact or a tidal interaction, or is a fragment of a recently disrupted progenitor. Another factor (relevant…
Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
We present in this communication a new solving procedure for Kelvin&Kirchhoff equations, considering the dynamics of falling the rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation…
Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS) while at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows for use of…
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…
Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in…
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…
Any swimmer embedded on a inertialess fluid must perform a non-reciprocal motion to swim forward. The archetypal demonstration of this unique motion-constraint was introduced by Purcell with the so-called "scallop theorem". Scallop here is…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating…