Superposition of Translational and Rotational Motions under Self-Propulsion of Liquid Marbles Filled with Aqueous Solutions of Camphor
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Self-locomotion of liquid marbles, coated with lycopodium or fumed fluorosilica powder, filled with a saturated aqueous solution of camphor and placed on a water/vapor interface is reported. Self-propelled marbles demonstrated a complicated motion, representing a superposition of translational and rotational motions. Oscillations of the velocity of the center of mass and the angular velocity of marbles, occurring in the antiphase, were registered and explained qualitatively. Self-propulsion occurs because of the Marangoni solutocapillary flow inspired by the adsorption of camphor (evaporated from the liquid marble) by the water surface. Scaling laws describing translational and rotational motions are proposed and checked. The rotational motion of marbles arises from the asymmetry of the field of the Marangoni stresses because of the adsorption of camphor evaporated from marbles.It is available to grasp the angular displacement of a human body for instruction on a sport performance. Provided the instantaneous angular velocity is known, the angular displacement may be obtained by the integration of it. However, although the angular velocity and the rotational axis of a rigid body can be easily derived, how should the angular velocity of a flexible body be defined? The main purpose of this paper is to define the angular velocity and the rotational axis of a whole flexible body system. A family of compact generalized formulations of rotational motion for a flexible body or multibody is derived by adopting an instantaneous rotational axis of the whole body. Here, the current angular momentum of the whole flexible system is equated with the sum of the individual angular momentum on each element over the system. As an example, simulation of a motion analysis of human body on a sport, especially throwing motion analysis of a shot put, is carried out in order to verify the derived equations in the paper
Angular acceleration
Circular motion
Constant angular velocity
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The treatment of rotations in rigid body and Cosserat solids dynamics is challenging. In most cases, at some point in the formulation, a parameterization of rotation is introduced and the intrinsic nature of the equations of motions is lost. Typically, this step considerably complicates the form of the equations and increases the order of the nonlinearities. Clearly, it is desirable to bypass parameterization of rotation, leaving the equations of motion in their original, intrinsic form. This has prompted the development of rotationless and intrinsic formulations. This paper focuses on the latter approach. The most famous example of intrinsic formulation is probably Euler’s second law for the motion of a rigid body rotating about an inertial point. This equation involves angular velocities solely, with algebraic nonlinearities of the second-order at most. Unfortunately, this intrinsic equation also suffers serious drawbacks: the angular velocity of the body is computed, but not its orientation, the body is “unaware” of its inertial orientation. This paper presents an alternative approach to the problem by proposing discrete statements of the rotation kinematic compatibility equation, which provide solutions for both rotation tensor and angular velocity without relying on a parameterization of rotation. The formulation is also generalized using the motion formalism, leading to very simple discretized equations of motion.
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Free surface
Surface stress
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This article covers rotational motion, angular velocity, instantaneous angular velocity, angular acceleration, mechanical motion, material point.
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Circular motion
Constant angular velocity
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Abstract Marangoni effect is a convective effect produced by surface tension gradient and has an important influence on the efficiency of hydrogen production by photoelectrochemical conversion. In this paper, COMSOL Multiphysics was used for numerical simulation to build a Marangoni effect model at the bubble interface in the photoelectrochemical conversion process, to clarify the mechanism of Marangoni effect of bubbles on the surface of photoelectrodes, and to discuss the influence of Marangoni effect on the process of bubble growth and separation. The results show that the thermal effect of light will cause the Marangoni convection around the bubbles and form a negative pressure zone at the root of the bubbles, which will attract the surrounding bubbles. Gravity has little effect on Marangoni convection, and an increase in the intensity of incoming light enhances the Marangoni effect. At the same time, Marangoni convection leads to a Marangoni force on the surface of the bubble, which prevents the bubble from leaving the surface of the photoelectrode.
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There is a numerical method presented that makes it possible to ensure the smoothness of the forming function defining the rotational motion of a multirotor unmanned aerial vehicle. Behavior of the generating function at the final integration step is investigated. The proposed method provides the formation of a rotational motion limited by the value of angular velocity with specified angular acceleration parameters. The numerical method was simulated when forming a virtual control signal for back-stepping control. The results of simulating the response to a step signal showed a decrease in consumed energy, an effective limitation of angular velocity and a significant decrease in the peak power consumption compared to the original back-stepping method with a slight increase in the transition process time. The values of virtual control parameters which ensure the formation of specified dynamic characteristics of the rotational motion of multirotor unmanned aerial vehicle were selected.
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Dynamics
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Aiming at the problem that the error modulation effects are affected by the angular motions of the vehicle in the dual-axis rotational laser gyro inertial navigation system (INS), a vehicle angular motion isolation method based on attitude feedback is proposed. Based on the error equations of INS, the principles of error modulation in rotation process are analyzed. Then the relationships between the navigation results and the controlled angular velocity imposed on the rotating mechanism are established. Finally, simulation models of angular motions with various forms are established. Simulation results show that this method can effectively isolate the angular motions of the vehicle and reduce the influences of the angular motions on the rotation modulation. The navigation accuracy is significantly improved.
Circular motion
Angular acceleration
Modulation (music)
Ring Laser Gyroscope
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Marangoni spreading driven by localized surfactant solution deposition previously has been studied only for single surfactant systems. For binary surfactant mixtures, interactions that generate surface tension synergism, a thermodynamic effect, may also synergistically enhance Marangoni spreading dynamics, introducing the concept of Marangoni synergism. Spreading dynamics and possible Marangoni synergism should depend not only on thermodynamic properties but also kinetic properties of the binary system.Tracer experiments that capture post-deposition surfactant front motion were performed in parallel with computational modeling, using binary surfactant pairs with varying interaction strengths. The model coupled the Navier-Stokes and advective diffusion equations with a Frumkin-type binary adsorption model.We confirm the existence of Marangoni synergism. Stronger binary surfactant attraction favors synergism in both surface tension reduction and Marangoni spreading. Binary composition ranges over which surface tension synergism occurs differ from those for Marangoni synergism, indicating that the origins of the two synergistic effects are not identical. Analysis of model spreading velocities show that the thermodynamic spreading parameter is the controlling factor at early times for both single and binary surfactant systems, while the intrinsic adsorption and desorption kinetics influence spreading velocities and thus the occurrence of Marangoni synergism at later times.
Marangoni number
Thermophoresis
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If the solid body makes a spatial motion, then at any point in time this motion can be decomposed into rotational at angular velocity and translational at linear velocity. The direction of the axis of rotation and the magnitude of the angular velocity, that is the vector of rotational motion at a given time does not change regardless of the point of the solid body (pole), relative to which the decomposition of velocities. For linear velocity translational motion is the opposite: the magnitude and direction of the vector depend on the choice of the pole. In a solid body, you can find a point, that is, a pole with respect to which both vectors of rotational and translational motions have the same direction. The common line given by these two vectors is called the instantaneous axis of rotation and sliding, or the kinematic screw. It is characterized by the direction and parameter - the ratio of linear and angular velocity. If the linear velocity is zero and the angular velocity is not, then at this point in time the body performs only rotational motion. If it is the other way around, then the body moves in translational manner without rotating motion. The accompanying trihedral moves along the directing curve, it makes a spatial motion, that is, at any given time it is possible to find the position of the axis of the kinematic screw. Its location in the trihedral, as in a solid body, is well defined and depends entirely on the differential characteristics of the curve at the point of location of the trihedral – its curvature and torsion. Since, in the general case, the curvature and torsion change as the trihedral moves along the curve, then the position of the axis of the kinematic screw will also change. Multitude of these positions form a linear surface - an axoid. At the same time distinguish the fixed axoid relative to the fixed coordinate system, and the moving - which is formed in the system of the trihedral and moves with it. The shape of the moving and fixed axoids depends on the curve. The curve itself can be reproduced by rolling a moving axoid over a fixed one, while sliding along a common touch line at a linear velocity, which is also determined by the curvature and torsion of the curve at a particular point. For flat curves, there is no sliding, that is, the movable axoid is rolling over a stationary one without sliding. There is a set of curves for which the angular velocity of the rotation of the trihedral is constant. These include the helical line too. The article deals with axoids of cylindrical lines and some of them are constructed.
Linear motion
Circular motion
Position (finance)
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