Study of the Rotational Motion of a Rigid Body in Profile School Elective Courses

2016 ◽  
Vol 4 (3) ◽  
pp. 40-45
Author(s):  
Харыбина ◽  
I. Kharybina ◽  
Новикова ◽  
Tatyana Novikova ◽  
Новиков ◽  
...  
Keyword(s):  
Rigid Body ◽  
Conservation Laws ◽  
Rotational Motion ◽  
School Level ◽  
Plane Parallel ◽  
Parallel Motion ◽  
Elective Courses ◽  
Formation Method ◽  
Instantaneous Center ◽  
Physics Course

The article deals with the problem of studying the rotational motion of a rigid body in a physics course at profi le school. It is proposed to supplement the study of the topic elective courses to meet the challenges of the kinematics, dynamics, conservation laws for describing plane-parallel motion of a solid body. The article gives examples of jobs on the formation method of fi nding instantaneous center of velocity, methods are provided for the activities of the students at the school level action.

scholarly journals Cases of integrability corresponding to the pendulummotion on the plane

2017 ◽  
Vol 21 (10) ◽  
pp. 91-113
Author(s):  
M.V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Field ◽  
Invariant Form ◽  
Motion Equations ◽  
Plane Parallel ◽  
Free Rigid Body ◽  
Parallel Motion ◽  
Tracking Force ◽  
Similar Force

In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconserva- tive force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

scholarly journals OPTIONS FOR PLANE-PARALLEL MOVEMENT OF GRAINS IN A SCRAPER CONVEYOR

2020 ◽  
Vol 14 (4) ◽  
pp. 96-99
Author(s):  
Sergey Yakhin ◽  
Il'gam Masalimov ◽  
Marat Nafikov ◽  
Ramis Mardanov
Keyword(s):  
Complex Motion ◽  
Sliding Speed ◽  
Friction Forces ◽  
Plane Parallel ◽  
Parallel Movement ◽  
Parallel Motion ◽  
Touch Point ◽  
Scraper Conveyor ◽  
Instantaneous Center ◽  
Kinematic Diagram

The kinematics of plane-parallel motion of a wheat or rye grain when moving in an inclined position in a scraper conveyor is considered. A kinematic diagram of the plane-parallel motion of the grain in the scraper conveyor was compiled, the position of the instantaneous center of the flat figure was determined, and options for the movement of grain in an inclined position at various possible positions of instantaneous center were considered. The profile of the grains is outlined by an elliptical curve. The point of contact of the elliptical profile of the caryopsis with the scraper makes a complex motion, while the horizontal speed of the scraper is portable for it, the sliding speed on the surface of the scraper is relative. The speed of the touch point of the grain with the pan is horizontal. For six possible positions of the instantaneous center, the directions of the velocities of the points of contact of the grains and the friction forces acting in them are determined. Grains of wheat or rye, moved in a scraper conveyor, in some cases can make plane-parallel movement. The point of contact of the elliptical profile of the caryopsis with the scraper makes a complex motion, while the horizontal speed of the scraper is portable for it, the sliding speed on the surface of the scraper is relative. The speed of the touch point 2 of the grain with the pan is horizontal.

Exponential control of a rotational motion of a rigid body using quaternions

2003 ◽  
Vol 137 (2-3) ◽  
pp. 195-207 ◽  
Author(s):  
Awad EL-Gohary ◽  
Ebrahim R. Elazab
Keyword(s):  
Rigid Body ◽  
Rotational Motion

scholarly journals The Rotating Rigid Body Model Based on a Non-twisting Frame

2020 ◽  
Vol 30 (6) ◽  
pp. 3199-3233 ◽  
Author(s):  
Cristian Guillermo Gebhardt ◽  
Ignacio Romero
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Conservation Laws ◽  
Rotation Rate ◽  
Governing Equations ◽  
New Model ◽  
Body Model ◽  
Integration Schemes ◽  
Rigid Body Model ◽  
Unit Vectors

Abstract This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations.

The Use of Projective Geometry on the Mechanism System Motion and Stability of the Special Problems in Judgement

2012 ◽  
Vol 482-484 ◽  
pp. 1041-1044
Author(s):  
Xiao Zhuang Song ◽  
Ming Liang Lu ◽  
Tao Qin
Keyword(s):  
Rigid Body ◽  
Projective Geometry ◽  
Euclidean Geometry ◽  
Specific Problem ◽  
Zero Point ◽  
Rigid Bodies ◽  
Parallel Connection ◽  
Fixed Plane ◽  
Instantaneous Center ◽  
Proof Of Principle

In a principle of kinematics, when a rigid body is motion in a plane, and the fixed plane only the presence of a speed zero point -- the instantaneous center of velocity. In the mechanism of two rigid bodies be connected by two parallel connection links, why can the continuous relative translation? Where is the instantaneous center of velocity? ... ... The traditional Euclidean geometry theory can’t explain these phenomenon, must use projective geometry theory to solve. The actual motion of the mechanism is disproof in Euclidean geometry principle limitation. This paper introduces the required in projective geometry basic proof of principle, and applied to a specific problem.

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