# Equations of motion

Xem 1-20 trên 91 kết quả Equations of motion
• ### Using the Lagrangian to obtain Equations of Motion

In Section 1.5 of the textbook, Zak introduces the Lagrangian L = K − U , which is the diﬀerence between the kinetic and potential energy of the system. He then proceeds to obtain the Lagrange equations of motion in Cartesian coordinates for a point mass subject to conservative forces, namely, d dt ∂L ∂ xi ˙ − ∂L = 0 i = 1, 2, 3. ∂xi (1)

• ### Successive algorithm for construction of equation of motion of constrained mechanical systems

The article devotes to t he construction of equations of motion of constrained mechanical systems. The constraint conditions are successively appended to the already defined systems. Therefore the algorithm is very flexible and allows studying the separate constraints more in detail. For illustration of consequent steps of the algorit hm one simple example is shown.

• ### A form of equation of motion for chaplyghin

In the present paper, a form of equations of motion for the Chaplyghin's systems is introduced. The scheme for writing these equations is very simple, because they are established by means of only the matrix of inertia of Lagrangian function and are written in the matrix form.

• ### An algorithm for deriving equations of motion of constrained mechanical system

The article deals with the form of equations of motion of mechanical system with constraints. For holonomic systems the number of differential equation is equal to the degrees of freedom, without regard to the number of chosen coordinates. The possibilities of computer processing (symbolical and numerical) are shown. Two simple examples demonstrate the described technique.

• ### A form of equation of motion of a mechanical system

The one of important problems of dynamics of a niultibody system its to establish automatically the equations of motion. In the present work it is constructed a form of equations of motion, which is useful for programming the problem of a multibody system, especially for applying the symbolic method in the automatical establishment of equations of motion of a multibody system.

• ### On modelling and simulation of a manipulator under consideration of a jammed joint

In this paper, the modelling of a jamming process of a joint during the operation of a manipulator is presented. Based on the kinematic property of a jamming process, a motion law of the jammed joint is chosen. By introducing a matrix coressponding to jammed joint, the equation of motion of the system is restructured without re-deriving. Some numerical simulations are carried out to illustrate the proposed algorithm.

• ### About the gibbs-appel equations for multibody systems

In this paper a matrix form of Gibbs-Appel function is recommended for multibody dynamics formulations. The form proposed in this paper seems to be more clear and suitable for automatic generation of dynamical equations of motion. The advantages followed from the formulation proppsed are illustrated through an example.

• ### A form of equations of motion of constrained mechanical systems

In the present paper a form of equations of motion of a constrained mechanical system is constructed. These equations only contain a minimum number of accelerations. In the other words, such equations are written in independent accelerations while the configuration of the system is described by dependent coordinates.

• ### A form of equations of motion of a mechanical system in quasi-coordinates

In the present paper the form of equations of motion is written in quasi-coordinates. These equations are solved with respect to quasi-accelerations, which allow to define the motion of a holonomic and nonholonomic systems by a closed set of algebraic - differential equations. The reaction forces of constraints imposed on the system under consideration are calculated by means of a simple algorithm.

• ### Motion Control Theory Needed in the Implementation of Practical Robotic Systems

Most research in robotics centers on the control and equations of motion for multiple link and multiple degree-of-freedom armed, legged, or propelled systems. A great amount of effort is expended to plot exacting paths for systems built from commercially available motors and motor controllers. Deficiencies in component and subsystem performance are often undetected until the device is well past the initial design stage.

• ### ON WEAK SOLUTIONS OF THE EQUATIONS OF MOTION OF A VISCOELASTIC MEDIUM WITH VARIABLE BOUNDARY V. G.

ON WEAK SOLUTIONS OF THE EQUATIONS OF MOTION OF A VISCOELASTIC MEDIUM WITH VARIABLE BOUNDARY V. G. ZVYAGIN AND V. P. ORLOV Received 2 September 2005 The regularized system of equations for one model of a viscoelastic medium with memory along trajectories of the ﬁeld of velocities is under consideration. The case of a changing domain is studied. We investigate the weak solvability of an initial boundary value problem for this system. 1. Introduction The purpose of the present paper is an extension of the result of [21] on the case of a changing domain. Let Ωt ∈ Rn , 2 ≤...

• ### Báo cáo " On equations of motion, boundary conditions and conserved energy-momentum of the rigid string "

The correct forms of the equations of motion, of the boundary conditions and of the reconserved energy - momentum for the a classical rigid string are given. Certain consequences of the equations of motion are presented. We also point out that in Hamilton description of ˙ the rigid string the usual time evolution equation F = {F, H} is modified by some boundary terms

• ### Ebook Introduction to continuum mechanics

Ebook Introduction to continuum mechanics has contents: Introduction, the notion of stress; budgets, fluxes, and the equations of motion; kinematics in continuum mechanics; elastic bodies; waves in an elastic medium, statics of elastic media, newtonian fluids, creeping flow, high reynolds number flow.

• ### Analytical solutions for bending, buckling and vibration analysis of functionally graded cylindrical panel

The main purpose of this article is to present analytical solutions for bending, buckling and free vibration analysis of cylindrical panel, which are composed of functionally graded materials (FGMs). Equations of motion are derived using Hamilton’s principle.

• ### Calculation of transonic flows around profiles with blunt and angled leading EDGES

Transonic flow is a mixed flow of subsonic and supersonic regions. Because of this mixture, the solution of transonic flow problems is obtained only when solving the differential equations of motion with special treatments for the transition from subsonic region to supersonic region and vice versa. We built codes solving the full potential equation and Euler equations by applying the finite difference method and finite volume method, and also associated with software Fluent to consider the viscous effects.

• ### Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory

In this paper, the free vibration of functionally sandwich grades plates with stiffeners is investigated by using the finite element method. The material properties are assumed to be graded in the thickness direction by a power-law distribution. Based on the third-order shear deformation theory, the governing equations of motion are derived from the Hamilton’s principle.

• ### Dynamics of a general multi axis robot with analytical optimal torque analysis

The robot equations of motion are obtained from the implemented program and verified against those obtained using only Lagrange equation. The output of program for the 3 DOF robot was used to find the optimal torque using analytical optimization analysis for a given set of parameters. This procedure analysis can be used as a benchmark analysis for any optimization technique.

• ### X-RAY SPECTROSCOPY

The next chapter presents an analytical solution for a nano-plate with Levy boundary conditions. The free vibration analysis is based on a first order shear deformation theory which includes the small scale effect. The governing equations of motion, reformulated as two new equations called the edge-zone and interior equations, are based on the nonlocal constitutive equations of Eringen.

• ### Chapter 9: Center of Mass and Linear Momentum

Finally we will use the conservation of linear momentum to study collisions in one and two dimensions and derive the equation of motion for rockets

• ### Equations of motion in the state and confiruration spaces

Consider a system with a single degree of freedom and assume that the equation expressing its dynamic equilibrium is a second order ordinary diﬀerential equation (ODE) in the generalized coordinate x.