Investigation of a New Formulation of the Lagrange Method for Constrained Dynamic Systems

1997 ◽  
Vol 64 (1) ◽  
pp. 116-122 ◽  
Author(s):  
A. Rosen ◽  
E. Edelstein
Keyword(s):  
Variational Methods ◽  
Dynamic Systems ◽  
Lagrange Multipliers ◽  
Nonholonomic Constraints ◽  
New Method ◽  
Lagrange Method ◽  
The Past ◽  
Stabilization Methods ◽  
Rigid Rod ◽  
New Formulation

Lagrange multipliers are often used in order to model constrained dynamic systems. This method results in problems of constraints violations and therefore various methods of constraints stabilization have been presented in the past. The purpose of the present paper is to present a new formulation of the method that stabilizes the constraints, but unlike other stabilization methods it is also consistent within the framework of variational methods. The new formulation can be applied to holonomic or nonholonomic constraints. After the presentation of the new formulation, its application to constrained rigid rod systems is presented. The results of the new method are compared with other stabilization techniques.

Children’s Lives and Deaths in Merovingian Gaul

2020 ◽  
pp. 185-213
Author(s):  
Émilie Perez
Keyword(s):  
Social Identity ◽  
Age Groups ◽  
New Method ◽  
Recent Analysis ◽  
Age And Gender ◽  
The Past ◽  
And Gender ◽  
Grave Goods

The role of children in Merovingian society has long been downplayed, and the study of their graves and bones has long been neglected. However, during the past fifteen years, archaeologists have shown growing interest in the place of children in Merovingian society. Nonetheless, this research has not been without challenges linked to the nature of the biological and material remains. Recent analysis of 315 children’s graves from four Merovingian cemeteries in northern Gaul (sixth to seventh centuries) allows us to understand the modalities of burial ritual for children. A new method for classifying children into social age groups shows that the type, quality, quantity, and diversity of grave goods were directly correlated with the age of the deceased. They increased from the age of eight and particularly around the time of puberty. This study discusses the role of age and gender in the construction and expression of social identity during childhood in the Merovingian period.

A Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems with Oil Residency Time Constraint

2014 ◽  
Vol 998-999 ◽  
pp. 1532-1535
Author(s):  
Yu Ming Zhao
Keyword(s):  
Crude Oil ◽  
Time Constraint ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Operation Sequencing ◽  
The Past ◽  
Time Formulation ◽  
New Formulation ◽  
Single Sequence ◽  
Residency Time

The optimal scheduling of crude-oil operation in refineries has been studied by various groups during the past decade leading to different mixed integer linear programming or mixed nonlinear programming formulations. This paper presents a new formulation with oil residency time constraint based on single-operation sequencing (SOS). It is different from previous formulations as it considers oil residency time constraint and pipeline transfer and does not require to postulate the number of priority-slots in which operations take place. This model is also based on the representation of a crude-oil scheduling by a single sequence of transfer operations. A simple MILP procedure has been used to solve this model leading to an satisfactory optimal result.

Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method. II. Applications for 2D SH case

1995 ◽  
Vol 85 (4) ◽  
pp. 1094-1106
Author(s):  
Xiaofei Chen
Keyword(s):  
Present Article ◽  
Analytical Solutions ◽  
Scattering Problem ◽  
Layered Media ◽  
Synthetic Seismograms ◽  
Numerical Results ◽  
New Method ◽  
New Formulation ◽  
Series Study

Abstract As the second part of a series study attempting to present a new method of seismogram synthesis for the irregular multi-layered media problems, the present article is devoted to discussing the aspects of the implementation of our new formulation developed earlier in part I of this series study (Chen, 1990). In this article, we have verified the validity of the formulation by comparing our numerical results with the existing analytical solutions for the scattering problem of a semi-circular canyon, and have shown its applicability by computing the synthetic seismograms for several selected irregular multi-layered media cases. Finally, applying our algorithm to the Whittier-Narrows earthquake of 1987, we have successfully interpreted the observed records.

scholarly journals The Integration of Radiocarbon Dating in Archaeology

Radiocarbon ◽  
1983 ◽  
Vol 25 (2) ◽  
pp. 639-644 ◽  
Author(s):  
H T Waterbolk
Keyword(s):  
Radiocarbon Dating ◽  
The Other ◽  
New Method ◽  
Time Range ◽  
Traditional Methods ◽  
Radiocarbon Dates ◽  
Fully Integrated ◽  
Expected Time ◽  
The Past

In the past 30 years many hundreds of archaeologic samples have been dated by radiocarbon laboratories. Yet, one cannot say that 14C dating is fully integrated into archaeology. For many archaeologists, a 14C date is an outside expertise, for which they are grateful, when it provides the answer to an otherwise insoluble chronologic problem and when it falls within the expected time range. But if a 14C date contradicts other chronologic evidence, they often find the ‘solution’ inexplicable. Some archaeologists are so impressed by the new method, that they neglect the other evidence; others simply reject problematic 14C dates as archaeologically unacceptable. Frequently, excavation reports are provided with an appendix listing the relevant 14C dates with little or no discussion of their implication. It is rare, indeed, to see in archaeologic reports a careful weighing of the various types of chronologic evidence. Yet, this is precisely what the archaeologist is accustomed to do with the evidence from his traditional methods for building up a chronology: typology and stratigraphy. Why should he not be able to include radiocarbon dates in the same way in his considerations?

scholarly journals The creative work of Sergey Paradzhanov as an event of Postmodernism

2009 ◽  
Vol 1 (1) ◽  
pp. 124-132
Author(s):  
Anna Georgievna Lukashova
Keyword(s):  
20Th Century ◽  
New Method ◽  
Past Century ◽  
Creative Work ◽  
The Past

In this article a new method of analysis of S. Paradzhanov's creative work is suggested: the works of Paradzhanov-artist and Paradzhanov-director are examined as a united paradigm, which gives an opportunity to present the phenomenon of his art in the context of art culture of the 20th century in the most adequate way, and deine the connection of the aesthetics of his work and the basic tendencies of the past century.

scholarly journals Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Coupled System ◽  
Weak Form ◽  
Integration Scheme ◽  
Motion Constraints ◽  
Multibody Dynamic ◽  
Time Integration Scheme

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

Computed Tomography and Biomechanical Comparison between Trans-Articular Screw Fixation and 2 Polymethylmethacrylate Cemented Constructs for Ventral Atlantoaxial Stabilization

2018 ◽  
Vol 31 (05) ◽  
pp. 344-355 ◽  
Author(s):  
Noël Moens ◽  
Luis Gaitero ◽  
Alex zur Linden ◽  
Fiona James ◽  
Gabrielle Monteith ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Screw Fixation ◽  
Biomechanical Properties ◽  
The Past ◽  
Stabilization Methods ◽  
Surgical Options ◽  
Atlantoaxial Stabilization ◽  
Ct Data ◽  
Biomechanical Comparison ◽  
Surgical Guidelines

Objectives Canine ventral atlantoaxial stabilization methods have been constantly evolving over the past few decades. Yet, proper experimental data comparing the feasibility and biomechanical properties of currently available surgical options are lacking. The aims of this study were (1) to describe and compare the safety profiles and biomechanical properties of three ventral atlantoaxial stabilization methods; and (2) to test whether recently reported optimal implant definitions constitute reasonable guidelines. Methods Three types of atlantoaxial stabilization including trans-articular screw fixation (TSF) and two cemented constructs (MI5 and MI6) were performed in 21 Beagle cadavers. Post-surgical computed tomography (CT) images of the constructs and biomechanical data were then generated and statistically analysed. Results The CT data revealed that TSF achieved significantly better apposition than cemented constructs. Out of 91 screws positioned, 4.4% were graded as dangerous and 86.8% as optimal. Optimal positioning was most challenging to obtain for mono-cortical screws. Analysis of biomechanical data suggested that all three techniques could likely achieve similar rates of atlantoaxial fusion when submitted to physiological loads but also that cemented constructs were less prone to failure compared with TSF. Clinical Significance This study provides evidence that all three techniques are technically feasible and biomechanically viable but also that the evaluated surgical guidelines could be improved.

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