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In this research, the rotation of a solid particle in a vortex flow is investigated computationally. The bvp4c MATLAB scheme is employed for mathematical modeling and physical analysis. After solving the governing equations, the influences of some physical parameters like initial values of radius, radial velocity and angular velocity as well as the ratio of drag force to inertia force on the velocity and displacement characteristics of the particle will be analyzed. The findings indicate that increasing $r_0$ and ${\omega }_0$ causes an increase in radial velocity, but increasing $u_0$ and ${\alpha }^2$ have conversed treatments. Also, the angular velocity enhances by increasing the ratio of drag-to-inertia forces.

In this paper, a computational method called the AGM technique is applied to solve the governing equations of a physical problem. This problem is related to the analysis of the motion of a spherical particle under the influences of a fluid flow. After solving the nonlinear equations using the Akbari–Ganji Method (AGM), the precision of outcomes is evaluated by comparing them with the numerical technique. The AGM demonstrates approximations with high accuracy to obtain the analytical solutions to the present problem. The results show that the velocity profiles have different trends with the increase of time, so the radial velocity decreases with time, still, the angular velocity increases with the increase of time.

In this paper, rotation properties of suspended particles under an external rotating electric field (EREF) are investigated. Based on the re-distribution of surface-induced charges on moving particles, the torque exerting on particles by EREF is derived analytically. Furthermore, for the sol suspended in Newtonian fluid, the angular velocity of the rotating particle is formulated by the EREF and the dielectric constants of the particle and matrix. The result shows that the angular velocity of particles depends on the angular velocity of EREF, and is proportional to the square of EREF strength. The maximum angular velocity of rotating particles is reached if the angular velocity of EREF is equal to the reciprocal of the relaxation time of the induced charge.

The general Euler-Poisson problem of rigid body motion is investigated. We study the three-dimensional algebraic level surfaces of the first integrals, and their topological bifurcations. The main result of this article is an analytical and qualitatively complete description of the projections of these integral manifolds to the body-fixed space of angular velocities. We classify the possible types of these invariant sets and analyze the dependence of their topology on the parameters of the body and the constants of the first integrals. Particular emphasis is given to the enveloping surfaces of the sets of admissible angular velocities. Their pre-images in the reduced phase space induce a Heegaard splitting which lends itself for a general choice of complete Poincaré surfaces of section, irrespective of whether or not the system is integrable.

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli’s function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second-order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.

The hydrodynamic dispersion of a solute in peristaltic flow of a reactive incompressible micropolar biofluid is studied as a model of chyme transport in the human intestinal system with wall effects. The long wavelength approximation, Taylor's limiting condition and dynamic boundary conditions at the flexible walls are used to obtain the average effective dispersion coefficient in the presence of combined homogeneous and heterogeneous chemical reactions. The effects of various pertinent parameters on the effective dispersion coefficient are discussed. It is observed that average effective dispersion coefficient increases with amplitude ratio which implies that dispersion is enhanced in the presence of peristalsis. Furthermore, average effective dispersion coefficient is also elevated with the micropolar rheological and wall parameters. Conversely dispersion is found to decrease with cross viscosity coefficient, homogeneous and heterogeneous chemical reaction rates. The present simulations provide an important benchmark for future chemo-fluid-structure interaction (FSI) computational models.

The structural principle of a novel silicon micromachined gyroscope, driven by the rotating carrier's angular velocity, is presented in this paper. The authors construct the mathematical module of the micromachined gyroscope and the dynamics parameters of the micromachined gyroscope are also analyzed and calculated. The signal detecting circuit of the micromachined gyroscope is described. The micromachined gyroscope uses capacitive variation to sense angular velocity and such operation principle is demonstrated in the paper. Then, the signal processing circuit of the micromachined gyroscope is analyzed in detail. Finally, the finite element analysis tool — ANSYS software is used to analyze the oscillation module and frequency response of the micromachined gyroscope. The theoretical research and computer imitation have certified that the structural principle of the silicon micromachined gyroscope driven by rotating carrier's angular velocity is correct.

In this paper, the in-plane free vibration analysis of the functionally graded rotating disks with variable thickness is presented utilizing DQM. It is assumed that the rotational velocity of the disk is constant and the thickness and material properties including modulus of elasticity and density vary along the radial coordinate. The distribution of the forward and backward traveling waves versus the angular velocity is demonstrated for several modal circles and nodal diameters with respect to the fixed and rotating coordinate systems. After presenting the accuracy and convergence of the numerical method, the derived formulation and the solution method are validated by comparing the results with those obtained in the literature for simple rotating disks. Furthermore, the critical speed of the rotating disk is introduced and obtained for different modes. Finally, the effects of the functionally graded index (describes the distribution of material properties) and geometric shape of the disks (thickness profile and radius ratio) on the natural frequencies and critical speed of the disk are presented. It is observed that as the number of nodal diameter increases, the critical speed of the disk consequently decreases and reaches to an asymptotic value. This value is independent of the geometric characteristics of the disk.

Flexion of the index finger is a fairly complex process requiring the coordination of different joints. This study is the first attempt to investigate how the angular velocity profile of the three right index joints (DIP, PIP, and MCP) varies with respect to time during the course of flexion. Ten right-handed subjects (healthy college students between 21 and 23 years old) were recruited to participate in the experiment. Each of these human subjects was instructed to perform a flexion task with his/her right hand. Five miniaturized (5-mm diameter) reflective markers were applied to each human subject: three placed at the DIP, PIP, and MCP joints of the index finger on the side close to thumb, and the rest at the predetermined landmarks on dorsum of thumb. A high-speed camera was used to record the motion of the index finger during a paced flexion, and the instantaneous angular velocity of each joint was determined by relating the marker displacement to the frame frequency (~5 ms between two consecutive frames). Opposite to the general belief that the speed is constant throughout a flexion cycle, to our best knowledge, this study, for the first time, has revealed that the speed of multi-joint movement actually varies with time. It has been identified that during one full flexion cycle, the angular velocity of the three joints of interest undergoes five distinguishable phases, referred as phases P1 (slow), P2 (fast), P3 (slow), P4 (fast), and P5 (slow), respectively. It has also been observed that duration of each of phases P1, P2, P4, or P5 accounts for approximately 10–15% of the whole flexion cycle, while P3 lasts for nearly half a cycle. Furthermore, although the flexions of DIP, PIP, and MCP joints cycle through the same five phases, the starts of their respective phases tend to vary. In P2 and P5, flexion of MCP takes place considerably later than those of PIP and DIP, whereas DIP flexes earlier than PIP in P2. The angular velocity of each joint reaches its peaks in P2 and P4; the peak velocity of DIP occurs earlier than that of PIP or MCP in P2, whereas peak of MCP is reached later than that of PIP. Moreover, the three joints of index finger flex with different angular velocities in each of the five phases: PIP moves significantly faster than MCP in P2, whereas DIP moves faster than MCP in P4. The results from our study indicate that the multi-joint motion of index finger is an uneven course, i.e. different joints flex with different angular velocities during the flexion. The temporal features of the velocity due to a single joint or multi-joint motion provide useful information to further clarify the dexterity of finger movement.