• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.8
• /
• pp.1303-1308
• /
• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of ail relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.893-898
• /
• 2004

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• Ocean Science Journal
• /
• v.43 no.4
• /
• pp.165-173
• /
• 2008

In this article, we describe a simple yet effective method for insertion of observational datasets in a mesoscale atmospheric model used in one-dimensional configuration through Nudging. To demonstrate the effectiveness of this technique, vertical profiles of meteorological parameters obtained from GLASS Sonde launches from a tiny island of Kaashidhoo in the Republic of Maldives are injected in a mesoscale atmospheric model - Advanced Regional Prediction System (ARPS), and model simulated parameters are compared with the available observational datasets. Analysis of one-time nudging in the model simulations over Kaashidhoo show that incorporation of this technique reasonably improves the model simulations within a time domain of +6 to +12 Hrs, while its impact on +18 Hrs simulations and beyond becomes literally null.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.12
• /
• pp.2156-2164
• /
• 1997

A new formulation for the dynamic analysis of constrained multibody systems is presented in this paper. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix introduced in this study : it can improve the efficiency of the formulation. Three numerical examples are given to demonstrate the accuracy and efficiency of the formulation.

• Journal of the Korean Society for Railway
• /
• v.2 no.1
• /
• pp.47-55
• /
• 1999

In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can be partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

• Journal of Mechanical Science and Technology
• /
• v.14 no.2
• /
• pp.159-167
• /
• 2000

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

• Proceedings of the KSR Conference
• /
• 1998.11a
• /
• pp.437-444
• /
• 1998

In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can he partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

• Structural Engineering and Mechanics
• /
• v.54 no.6
• /
• pp.1153-1174
• /
• 2015

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

• International journal of advanced smart convergence
• /
• v.2 no.1
• /
• pp.21-23
• /
• 2013

The antenna pattern in this case has a main beam pointed in the desired signal direction, and has a null in the direction of the interference.The conventional antenna pattern concepts of beam width, side lobes, and main beams are not used, as the antenna weights are designed to achieve a set performance criterion such as maximization of the output SNR.A new direction of arrival estimation method using effects of model errors and sensitivity analysis is proposed. Two subspaces are used to form a signal space whose phase shift between the reference signal and its effects of model error signal. Through simulation, the performance showed that the proposed method leads to increased resolution and improved accuracy of DOA estimation relative to those achieved with existing method. Since a desired signal is obtained after interference rejection through correction effects of model error, the effect of channel interference on the estimation is significantly reduced.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.171-184
• /
• 2014

A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.