scholarly journals Closure to “Discussion of ‘On Energy Rate Theorems for Linear First-Order Nonholonomic Systems’” (1992, ASME J. Appl Mech., 59, pp. 241–242)

1992 ◽  
Vol 59 (1) ◽  
pp. 242-242
Author(s):  
John G. Papastavridis
Keyword(s):  
Nonholonomic Systems ◽  
Energy Rate ◽  
First Order

On Energy Rate Theorems for Linear First-Order Nonholonomic Systems

1991 ◽  
Vol 58 (2) ◽  
pp. 536-544 ◽  
Author(s):  
John G. Papastavridis
Keyword(s):  
Recent Work ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Systems ◽  
General Linear ◽  
Energy Rate ◽  
First Order ◽  
Power Equation ◽  
Boltzmann Hamel Equations ◽  
Power Reaction

Starting with the Boltzmann/Hamel equations of motion of mechanical systems subject to general linear and first-order nonholonomic and rheonomic constraints, and in nonholonomic coordinates, this paper derives the general (reactionless) energy rate, or power, equation for such systems, in a straightforward and physically clear fashion. A power (reaction-containing) equation for these systems, but in holonomic coordinates, is also derived for completeness. An example of a sphere rolling on a uniformly spinning plane serves to illustrate these power theorems. The paper extends and corrects the recent work by Kane and Levinson (1988) on the same topic.

On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems

1993 ◽  
Author(s):  
Timothy A. Loduha ◽  
Bahram Ravani
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Relaxation Method ◽  
Nonholonomic Systems ◽  
Dynamical Equations ◽  
Generalized Coordinates ◽  
First Order ◽  
Constraint Relaxation ◽  
Constrained Dynamical Systems ◽  
Generalized Coordinate

Abstract In this paper we present a method for obtaining first-order decoupled equations of motion for multi-rigid body systems. The inherent flexibility in choosing generalized velocity components as a function of generalized coordinates is used to influence the structure of the resulting dynamical equations. Initially, we describe how a congruency transformation can be formed that represents the transformation between generalized velocity components and generalized coordinate derivatives. It is shown that the proper choice for the congruency transformation will insure generation of first-order decoupled equations of motion for holonomic systems. In the case of nonholonomic systems, or more complex dynamical systems, where the appropriate congruency transformation may be difficult to obtain, we present a constraint relaxation method based on the use of orthogonal complements. The results are illustrated using several examples. Finally, we discuss numerical implementation of congruency transformations to achieve first-order decoupled equations for simulation purposes.

On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems

1995 ◽  
Vol 62 (1) ◽  
pp. 216-222 ◽  
Author(s):  
T. A. Loduha ◽  
B. Ravani
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Numerical Implementation ◽  
Dynamical Equations ◽  
Generalized Coordinates ◽  
First Order ◽  
Holonomic Systems ◽  
Constrained Dynamical Systems ◽  
Generalized Coordinate

In this paper we present a method for obtaining first-order decoupled equations of motion for multirigid body systems. The inherent flexibility in choosing generalized velocity components as a function of generalized coordinates is used to influence the structure of the resulting dynamical equations. Initially, we describe how a congruency transformation can be formed that represents the transformation between generalized velocity components and generalized coordinate derivatives. It is shown that the proper choice for the congruency transformation will insure generation of first-order decoupled equations of motion for holonomic systems. In the case of nonholonomic systems, or holonomic systems with unreduced configuration coordinates, we incorporate an orthogonal complement in conjunction with the congruency transformation. A pair of examples illustrate the results. Finally, we discuss numerical implementation of congruency transformations to achieve first-order decoupled equations for simulation purposes.

scholarly journals Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1337
Author(s):  
Masahide Ito
Keyword(s):  
Motion Planning ◽  
Nonholonomic Systems ◽  
Second Order ◽  
Literature Survey ◽  
First Order ◽  
Underactuated Manipulator ◽  
Planning Algorithm ◽  
The One ◽  
Specific Control ◽  
Form System

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Morphological studies of linear (AB)n multiblock copolymers and their blends

1992 ◽  
Vol 50 (1) ◽  
pp. 384-385
Author(s):  
Richard J. Spontak ◽  
Steven D. Smith ◽  
Arman Ashraf
Keyword(s):  
Electron Microscopy ◽  
Microphase Separation ◽  
Multiblock Copolymers ◽  
First Order ◽  
Morphological Studies ◽  
Transmission Electron ◽  
First Order Phase Transition ◽  
Covalently Bonded ◽  
Total Molecular Weight ◽  
First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

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