Sharif Digital Repository

A generalized coordinates molecular Hamiltonian for polyatomic molecules has been obtained. Using this Hamiltonian in Radau coordinates as the orthogonal coordinates, the molecular Hamiltonian is derived for tri-atomic molecules. An exact derivation is presented of the molecular Hamiltonian in different axis embedding such as bond embedding, bisector embedding, and the linear combination of Radau vector coordinates. In addition, the symmetrized Radau coordinates are considered as an example for this general formulation. This new approach is greatly simplified. Also presented are simple and explicit expressions without cross-terms in Radau coordinates as vibrational variables  

In this paper we have presented a new form of Kane's equations. This new form is expressed in the matrix form with the components of partial derivatives of linear and angular velocities relative to the generalized speeds and generalized coordinates. The number of obtained equations is equal to the number of degrees of freedom represented in a closed form. Also the equations can be rearranged to appear only one of the time derivatives of generalized speeds in each equation. This form is appropriate especially when one intends to derive equations recursively. Hence in addition to the simplicity, the amount of calculations is noticeably reduced and also can be used in a control unit. Copyright... 

Traditional electromyography-assisted optimization (TEMG) models are commonly employed to compute trunk muscle forces and spinal loads for the design of clinical/treatment and ergonomics/prevention programs. These models calculate muscle forces solely based on moment equilibrium requirements at spinal joints. Due to simplifications/assumptions in the measurement/processing of surface EMG activities and in the presumed muscle EMG-force relationship, these models fail to satisfy stability requirements. Hence, the present study aimed to develop a novel stability-based EMG-assisted optimization (SEMG) method applied to a musculoskeletal spine model in which trunk muscle forces were estimated by... 

The transformation of the complete (non-relativistic) molecular Hamiltonian from Cartesian to generalized coordinates based on the tensor form has been obtained. By taking generalized internal coordinates depending on two parameters we present an exact derivation of the molecular Hamiltonian that has simple and explicit expressions for general triatomic molecules, and all rovibrational couplings are determined. Our approach is applicable to various kinds of internal coordinates in a straightforward way. In this derivation, no approximations and no restrictions are imposed on the nature of the vibrational variables. We also introduce a straightforward method with minimum equations to obtain... 

The attitude fault-tolerant control of a flexible satellite actuated by reaction wheels and magnetic torquer bars is investigated in this article. A low earth orbit is considered for moment perturbations such as drag and gravity gradient. Furthermore, the flexible panels attached to a rigid central body are modeled through the assumed mode approach by a finite set of bending modal motion. The ordinary differential equations of their generalized coordinates are found using Lagrange’s equation, and the resulting dynamical model is validated by comparing its simulation results to the NX Siemens software results. Finally, a fault-tolerant controller based on sliding mode control is suggested and... 

Flight dynamics of the guided vehicle is modelled by the aid of linear and angular equations of motions using Lagrange's approach in this paper. Governing equations of the control system and the elastic behavior of the vehicle are added to the equations of dynamic states. Flexibility effect is modelled using the normal modes, generalized coordinates and forces. For validation of modified FORTRAN simulation code, the stability of specific vehicles is determined and compared with the same results in the literature. Using this code and by solving the governing equations for the desired flight vehicle, the aeroservoelasticity is analyzed and then the results are compared with the rigid cases and... 

Aeroelastic stability of a flexible supersonic flight vehicle is considered using nonlinear dynamics, nonlinear aerodynamics, and a linear structural model. Response surfaces including global multivariate orthogonal modeling functions are invoked to derive applied nonlinear aerodynamic coefficients. A modified Gram-Schmidt method is utilized to orthogonalize the produced polynomial multivariate functions, selected and ranked by predicted squared error metric. Local variation of angle-of-attack and side-slip angle is applied to the analytical model. Identification of nonlinear aerodynamic coefficients of the flight vehicle is conducted employing a CFD code and the required analytical model... 

We present a novel method for deriving the governing equations of the musculoskeletal system, a new class of multibody systems in which the constituent components are connected together via anatomical joints which behave differently compared with traditional mechanical joints. In such systems, the kinematics of the joints and the corresponding constraints are characterized experimentally. We generate the equations of motion of these complex systems in which the homogeneous transformation matrices become matrix-valued functions of the generalized coordinate vector due to the empirical expression of body coordinates as smooth functions of generalized coordinates. The detailed mathematical... 

Despite their simple structure and design, microcantilevers are receiving increased attention due to their unique sensing and actuation features in many MEMS and NEMS. Along this line, a non-linear distributed-parameters modeling of a microcantilever beam under the influence of a nanoparticle sample is studied in this paper. A long-range Van der Waals force model is utilized to describe the microcantilever-particle interaction along with an inextensibility condition for the microcantilever in order to derive the equations of motion in terms of only one generalized coordinate. Both of these considerations impose strong nonlinearities on the resultant integro-partial equations of motion. In...