Gravitation and the Unified Nature of All Kinds of Motion in Non-Empty Space (Part 1)

The presented work examines the mechanism and conditions of self-motion in bodies as systems of interacting elements. It is shown how the oscillation parameters of these elements determine the mode of motion of the system (body). In this case, the motion is considered as a consequence of symmetry breaking of forces in the systems themselves, and not as a reaction of individual elements to external influences. It is shown that such a violation takes place both in the gravitational field and when the system moves by inertia. Examples of the influence of changes in phase (φ) and frequency (f) parameters of the system elements on the velocity mode of its motion in space are considered. The identity of the causes of self-motion is revealed both in the case of gravitation and inertial motion.

Radiographic Circularity of Capitellum and Its Relation to the Range of Motion

Background: The shape of the capitellum has been traditionally described in anatomy books as part of a sphere. Alteration in the capitellar morphology following pathologies such as fractures, osteochondrosis, and degenerative arthritis has been associated with less optimum functional results. Aim: To define the relationship between the sphericity of the capitellar morphology as measured on trauma series plain radiographs and the elbow range of motion. Methods: 40 patients were included in the study. All patients recruited from the upper limb clinics presented with non-elbow joint-related complaints. The elbow range of motion was measured using a standardized technique. Digital anteroposterior and lateral radiographs of patients’ elbows were used to measure capitellar circularity using the ImageJ processing program and circularity calculation equation. Correlation analyses were conducted between the degree of capitellar sphericity and elbow range of motion. Results: The results of measurements from the anteroposterior radiographs showed a positive correlation between increased circularity and an increase in the range of flexion, pronation, and supination. The range of extension decreased with the increased circularity of the capitellum. This trend was repeated with measures of lateral radiographs but was statistically not significant. Conclusion: Native capitellar circularity has an impact on the elbow range of motion. This should be put into consideration when dealing with pathologies that affect capitellar morphology.

The resistive range of motion exercise training in Duchenne muscular dystrophy:a case study

Background:To determine the effectiveness of resistive range of motion exercises in improving muscle strength and functional abilities in Duchenne muscular dystrophy.The study was also aimed to determine if resistive range of motion exercises can slow down the progression of the disease.Methods:A seven-year-old male child was diagnosed with Duchenne muscle dystrophy presented to outpatient physiotherapy clinic.The patient was presented with difficulty in stair climbing,sitting up from the floor,fatigue,and muscle weakness specifically weakness in the proximal limb muscles.The progressive resistive range of motion training was implemented for four years to improve muscle strength and functional abilities.The medical research council grading scale,north ambulatory assessment scale,and creatine kinase were used to evaluate muscle strength,functional abilities,and creatine kinase levels.Results:The muscular strength and functional abilities did not improve after four years of exercise training.The creatine kinase levels were decreased over the period of four years.Conclusion:Resistive range of motion exercises are helpful in maintaining the muscular strength and functional abilities in Duchenne muscular dystrophy.

Measurement of cervical range of motion using smartphone compass in the healthy people:a cross-sectional pilot study

Objective:This study evaluates the reliability of smartphone compass software in measuring the cervical range of motion in healthy people.Methods:We selected 40 healthy intern college students from Tianjin Hospital from June to August 2022 to participate in this study.Two physiotherapists used a smartphone(iPhone 11256 Gb(model A2223))compass software to measure six directions of motion of the cervical spine in 40 subjects in a total of 3 rounds each.The intraclass correlation coefficient was used to compare the reliability intra-group,and the Pearson correlation coefficient was also used to compare the correlation between groups,with P<0.05 being statistically significant.Results:The intraclass correlation coefficient showed good reliability(>0.5)in cervical range of motion(CROM),especially in cervical flexion and right rotation(>0.9).In the correlation comparison between the two groups,the Spearman comparison was used,and the six directions of the cervical spine were significantly correlated(P<0.05).Conclusion:The built-in compass software in smartphones has good reliability in measuring CROM in healthy people.

Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy

To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.

Forward flight of a model butterfly: Simulation by equations of motion coupled with the Navier-Stokes equations

The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows： （1） The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. （2） Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. （3） The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.

Stability of Motion for Generalized Birkhoffian Systems

The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.

Stability of motion state and bifurcation properties of planetary gear train

A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.

A Robotic System with Robust Remote Center of Motion Constraint for Endometrial Regeneration Surgery

Surgical robots have been widely used in diferent procedures to improve and facilitate the surgery.However,there is no robot designed for endometrial regeneration surgery,which is a new therapy for restoring fertility in women using stem cells.Endometrial regeneration surgery requires processing of the endometrium and transplantation of stem cells with minimal trauma to the uterus.In this paper,we introduce a surgical robotic system that consists of a dexterous hysteroscope,supporting arm,and additional novel instruments to facilitate the operation and decrease trauma to the uterus.Remote center of motion(RCM)constraint is required to protect the cervix of the uterus.First,the supporting arm and hysteroscope are controlled separately in kinematics to ensure that the RCM constraint and hysteroscope’s shape and posture are predictable.Then,a task-decoupled method is used to improve the robustness of the RCM constraint.Experiments confrm that the proposed method is more robust and achieves higher RCM accuracy.In addition,the master-slave control of a robot with RCM constraint is also verifed.This study proposes the realization of a robot with robust RCM control for endometrial regeneration surgery.

EQUATIONS OF MOTION FOR NONHOLONOMIC MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.

EQUATIONS OF MOTION AND BOUNDARY CONDITIONS OF INCREMENTAL RATE TYPE FOR POLAR CONTINUA

The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.

Effects of Degrees of Motion Freedom on Free-Fall of A Sphere in Fluid

Free-fall of a sphere in fluid is investigated at a Galileo number of 204 by direct numerical simulations(DNS). We mainly focus on the effects of different degrees-of-freedom(DOFs) of the sphere motion during free-fall. The characteristics of free-fall are compared with those of flow past a fixed sphere. Additional numerical tests are conducted with constraints placed on the translational or rotational DOFs of the sphere motion to analyze different DOFs of sphere motion. The transverse motion contributes significantly to the characteristics of free-fall; it results in the retardation of the vortex shedding, leading to the decrease of the Strouhal number. In addition, the transversal sphere motion exhibits the tendency to promote the sphere rotation. On the contrary, the effects of the sphere rotation and vertical oscillations during free-fall are negligible.

Charge Couple Device-Based Systemfor3-di mensional Real Ti me Positioning on the Assessment of Segmental Range of Motion of Lumbar Spine

Objective： To observe the tested results of the segmental range of motion （ROM） of lumbar spine by charge couple device （CCD）-based system for 3-dimensional real-time positioning （CCD system）, and to analyze its clinical significance. Methods： Seven patients with lumbar joint dysfunction and 8 healthy subjects were tested twice by the CCD-based system with an interval of 10 min. Results： The ROM of the patients was obviously lesser than that of the healthy subjects. The measuring data of segmental ROM of lumbar spine by CCD system is correlated significantly to the same data checked later on the same subjects in every direction of the movements. The differences between two checks are usually less than 1 degree. Conclusion： Specially designed CCD based system for 3-dimensional real-time positioning could objectively reflect the segmental ROM of lumbar spine. The system would be of great clinical significance in the assessment of the biomechanical dysfunction of lumbar spine and the effect of the treatment applied.

A FIELD METHOD FOR INTEGRATING THE EQUATIONS OF MOTION OF NONHOLONOMIC CONTROLLABLE SYSTEMS

This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.

Mixed Quantum Classical Reaction Rates based on the Phase Space Formulation of the Hierarchical Equations of Motion

In a previous work[J.Chem.Phys.140,174105(2014)],we have shown that a mixed quantum classical(MQC)rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions.However,the method is based on the high temperature approximation of the hierarchical equation of motion(HEOM)with the Debye-Drude spectral density,and results in a multistate Zusman type of equation.We now extend this theory to include quantum effects of the bath degrees of freedom.By writing the full HEOM into a multidimensional partial differential equation in phase space,we can define a new reaction coordinate,and the previous method can be generalized to the full quantum regime.The validity of the new method is demonstrated by using numerical examples,including the spin-Boson model,and the double well model for proton transfer reaction.The new method is found to resolve some key problems of the previous theory based on high temperature approximation,including possible numerical instability in long time simulation and wrong rate constant at low temperatures.

ONE TYPE OF INTEGRALS FOR THE EQUATIONS OF MOTION OF HIGHER-ORDER NONHOLONOMIC SYSTEMS

This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.

AN EQUATION OF MOTION FOR A THICK VISCOELASTIC PLATE

In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d＇Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d＇Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.