scholarly journals A New Approach in Analytical Dynamics of Mechanical Systems

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 95 ◽  
Author(s):  
Iuliu Negrean ◽  
Adina-Veronica Crișan ◽  
Sorin Vlase
Keyword(s):  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Matrix Form ◽  
Final Part ◽  
Analytical Dynamics ◽  
Research Papers ◽  
New Approach ◽  
D’Alembert Principle ◽  
Matrix Exponentials

This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.

New Formulations on Acceleration Energies in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 43-48
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Dynamic Study ◽  
Final Part ◽  
Transient Phase ◽  
Dynamic Aspect ◽  
Analytical Dynamics ◽  
Time Variations

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

New Formulations on Motion Equations in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 49-54 ◽  
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Higher Order ◽  
Analytical Dynamics ◽  
Lagrange Principle ◽  
Motion Equations ◽  
Differential Motion

Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

The Principles of Equity & Trusts

2018 ◽  
Author(s):  
Graham Virgo
Keyword(s):  
New Zealand ◽  
Common Law ◽  
Fiduciary Duty ◽  
Final Part ◽  
New Approach ◽  
The Subject ◽  
The Law ◽  
Contemporary Context

The Principles of Equity & Trusts offers a new approach to this dynamic area of law. This book examines the law of Equity and Trusts in its contemporary context, offering a critical and insightful commentary on the law, its application, and development. The text communicates both Equity and trust doctrine and also theory and reflects the modern understanding of the subject, as propounded both by the judiciary and commentators in England and other Common Law jurisdictions, notably Australia, Canada, New Zealand, and Singapore. The book consists of nine parts. Part I considers the history and contemporary relevance of Equity. Part II is about the express trust. Part III considers purpose trusts. Part IV then examines implied trusts. Part V is about beneficiaries. Part VI examines trustees’ powers and duties. Part VII examines variations of trusts. Part VIII is about breach of trust and fiduciary duty and the personal and proprietary remedies available for such breach. The final part examines other equitable remedies.

On the Equilibrium Conditions of Nonstationary Mechanical Systems

1999 ◽  
Vol 66 (4) ◽  
pp. 937-939
Author(s):  
M. Kazic ◽  
R. Bulatovic
Keyword(s):  
Equilibrium Problem ◽  
Virtual Work ◽  
Mechanical Systems ◽  
Principle Of Virtual Work ◽  
Equilibrium Conditions ◽  
New Approach ◽  
Starting Point ◽  
Stationary Problems ◽  
Nonstationary Systems

The equilibrium problem of nonstationary systems is studied. The starting point is the principle of virtual work (PVW). Contrary to stationary problems, some additional conditions (along with PVW) should be satisfied. Proof of Gantmacher’s postulate is derived. A new approach is given, and some results of other authors are discussed.

scholarly journals Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1077 ◽  
Author(s):  
Negrean ◽  
Crișan
Keyword(s):  
Multibody Systems ◽  
Driving Forces ◽  
Higher Order ◽  
Analytical Mechanics ◽  
Polynomial Functions ◽  
Control Functions ◽  
Generalized Variables ◽  
The Matrix ◽  
Matrix Exponentials ◽  
Fifth Order

The present paper’s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have undeniable advantages in the matrix study of any complex mechanical system. The present paper proposes some new approaches, based on differential principles from analytical mechanics, by using some important dynamics notions, regarding the acceleration energies of the first, second and third order. This study extended the equations of the higher order, which provide the possibility of applying the initial motion conditions in the positions, velocities and accelerations of the first and second order. In order to determine the time variation laws for the generalized variables, the driving forces and acceleration energies of the higher order are applied by the time polynomial functions of the fifth order. According to inverse kinematics also named control kinematics of the robots, the applications of polynomial functions lead to the kinematic control functions of mechanical motions, especially the transitory motions. They influence the dynamic behavior of multibody systems, in which robot structures are included.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems—Extensions for Higher-Order Continuum Models

1998 ◽  
Vol 120 (1) ◽  
pp. 142-144 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Higher Order ◽  
Constrained Motion ◽  
Momentum Exchange ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Boundary Equations ◽  
Hybrid Differential Equations

In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems (HPMBS) undergoing contact/impact motion. The method rigorously models all motion regimes of hybrid multiple body systems (i.e., free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations; Lagrange multipliers are not required. The contact/impact regime was modeled via the idea of instantaneously applied nonholonomic constraints. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this technical brief, the above-mentioned method is extended to include the higher-order continuum assumptions which eliminates the continuum shortfalls from the previous work. The main contributions of this work include: 1) the previous work is rigorously extended, and 2) the fact that coefficients of restitution are not required for modeling the momentum exchange between motion regimes of HPMBS. The field and boundary equations provide the needed extra equations that are used to supply post-collision pointwise relationships for the generalized velocities and velocity fields.

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