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Control of a Bicycle Using Virtual Holonomic Constraints  [PDF]
Luca Consolini,Manfredi Maggiore
Mathematics , 2013,
Abstract: The paper studies the problem of making Getz's bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method. Specifically, a VHC is enforced making the roll angle of the bicycle become a function of the bicycle's position along the curve. It is shown that the VHC can be automatically generated as a periodic solution of a scalar periodic differential equation, which we call virtual constraint generator. Finally, it is shown that if the curve is sufficiently long as compared to the height of the bicycle's centre of mass and its wheel base, then the enforcement of a suitable VHC makes the bicycle traverse the curve with a steady-state speed profile which is periodic and independent of initial conditions. An outcome of this work is a proof that the constrained dynamics of a Lagrangian control system subject to a VHC are generally not Lagrangian.
Bicycle Level of Service Evaluation Method for Urban Road Segment  [PDF]
Shinan Shu, Yang Bian, Jian Rong, Shuang Li
Open Journal of Applied Sciences (OJAppS) , 2018, DOI: 10.4236/ojapps.2018.82007
Abstract: As a sustainable mode of transportation, bicycles significantly improve daily mobility. In order to provide theoretics support for improvement of the bicycling environment, this paper proposed bicycle level of service (BLOS) evaluation method for urban road segment according to cyclists’ perception. First, influence factors of BLOS were identified from aspects of road facility, traffic characteristics, and environmental condition. Second, bicycling videos were recorded and a satisfaction survey was conducted. Four BLOS evaluation models for different separation facilities were established. Last, bicycling behavioral stages of travelers were divided based on the transtheoretical model. A new BLOS classification criterion was proposed according to travelers’ demand of different stages.
S. Sunay Y?ld?r?m DO?RU,?zgül Bike Yücalan ?NAL,Hafizullah BEK
Selcuk Universitesi Sosyal Bilimler Enstitusu Dergisi , 2007,
Abstract: The aim of this research was to examining the effectiveness of using direct instructionmethod for teaching of balance wheeled bicycle riding ability to the autistic children. In order toresearch this aim a teaching method composing of activities increasing attention control andpsycho-motor abilities was used. Participants were 3 male autistic children. In this research, directinstruction method was used in order to teach the ability of riding balance wheeled bicycle. Theautistic children were trained individually in an organized and controlled environment. At theend of the study, the data such as generalization, observation, application and reliability ofobservers were gathered. According to the results of the study, all the 3 autistic childrendeveloped the ability of riding a balance wheeled bicycle.
Ergonomic Analysis of UI Bicycle Using Posture Evaluation Index (PEI) Method in Virtual Environment
Erlinda Muslim,Liza Afrinotha,Zulkarnain,Boy Nurtjahyo
Makara Seri Teknologi , 2010,
Abstract: Ergonomic Analysis of UI Bicycle Using Posture Evaluation Index (PEI) Method in Virtual Environment. This research was conducted to study ergonomic aspect from University of Indonesia bicycle in virtual environment. Software Jack 6.0 was used to analyze it. PEI was used as approach that integrated the results of three methods: Lower Back Analysis, Ovako Working Posture Analysis, and Rapid Upper Limb Assessment. The research objective is to evaluate existing design of University of Indonesia bicycle and to determine the most ergonomic redesign which concern with handlebar height and saddle height modification. The result showed that the most ergonomic design of University of Indonesia bicycle is the one with the highest handlebar height (22 cm) and the lowest saddle height (11 cm).
A New Lagrangian Multiplier Method on Constrained Optimization  [PDF]
You-Lin Shang, Sheng-Li Guo, Xiang-Yi Jiang
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.330198
Abstract: In this paper, a new augmented Lagrangian function with 4-piecewise linear NCP function is introduced for solving nonlinear programming problems with equality constrained and inequality constrained. It is proved that a solution of the original constrained problem and corresponding values of Lagrange multipliers can be found by solving an unconstrained minimization of the augmented Lagrange function. Meanwhile, a new Lagrangian multiplier method corresponding with new augmented Lagrangian function is proposed. And this method is implementable and convergent.
Limitations of the method of Lagrangian Descriptors in incompressible flows  [PDF]
Alfonso Ruiz-Herrera
Mathematics , 2015,
Abstract: The method of Lagrangian descriptors has been already applied in many different contexts, specially in geophysical flows. In this paper we analyze the performance of this methodology in incompressible flows. We demonstrate that barriers to transport are not always coded by singular features of the $M$ function as Mancho, Wiggins and their co-workers conjectured. The techniques presented here are not restricted to incompressible flows. In fact, by our approach, one can infer that the method of Lagrangian descriptors is not useful in most linear systems.
Solar Bicycle  [PDF]
International Journal of Engineering Science and Technology , 2011,
Abstract: The running costs of the present vehicles are rising day by day hence common man is looking for an alternate mode of transport, with low fuel and maintenance cost. Solar bicycle is an attempt to meet these needs. It is an environmentally sustainable and zero running cost vehicle. It uses photovoltaic cells to absorb energy from sunlight. The absorbed energy is stored in battery. The hub motor mounted on the rear wheel uses this energy to run the cycle. A fully charged battery gives a mileage of 15-20 km. It is also provided with manual pedaling which increases the cycle’s mileage further. Average speed of the cycle is 15-18 kmph.
New Convergence Properties of the Primal Augmented Lagrangian Method  [PDF]
Jinchuan Zhou,Xunzhi Zhu,Lili Pan,Wenling Zhao
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/902131
Abstract: New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally. 1. Introduction In this paper, we consider the following nonlinear programming problem: where for each and for each are all continuously differentiable functions, is a nonempty and closed set in . Denoted by the feasible region and by the solution set. Augmented Lagrangian algorithms are very popular tools for solving nonlinear programming problems. At each outer iteration of these methods, a simpler optimization problem is solved, for which efficient algorithms can be used, especially when the problems are large. The most famous augmented Lagrangian algorithm based on the Powell-Hestenes-Rockafellar [1–3] formula has been successfully used for defining practical nonlinear programming algorithms [4–7]. At each iteration, a minimization problem with simple constraints is approximately solved whereas Lagrange multipliers and penalty parameters are updated in the master routine. The advantage of the Augmented Lagrangian approach over other methods is that the subproblems can be solved using algorithms that can deal with a very large number of variables without making use of factorization of matrices of any kind. An indispensable assumption in the most existing global convergence analysis for augmented Lagrangian methods is that the multiplier sequence generated by the algorithms is bounded. This restrictive assumption confines applications of augmented Lagrangian methods in many practical situation. The important work on this direction includes [8], where global convergence of modified augmented Lagrangian methods for nonconvex optimization with equality constraints was established; and Andreani et al. [4] and Birgin et al. [9] investigated the augmented Lagrangian methods using safeguarding strategies for nonconvex constrained problems. Recently, for inequality-constrained global optimization, Luo et al. [10] established the convergence properties of the primal-dual method based on four types of augmented Lagrangian functions without the boundedness assumption of the
On the discrete bicycle transformation  [PDF]
Serge Tabachnikov,Emmanuel Tsukerman
Mathematics , 2012,
Abstract: We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transformation. Working toward establishing complete integrability of the discrete bicycle transformation, we describe the monodromy integrals and prove the Bianchi permutability property. We show that the discrete bicycle transformation commutes with the recutting of polygons, a discrete dynamical system, previously studied by V. Adler. We show that a certain center associated with a polygon and discovered by Adler, is preserved under the discrete bicycle transformation. As a case study, we give a complete description of the dynamics of the discrete bicycle transformation on plane quadrilaterals.
Basic Theorem, Gauge Algebra, $θ$-superfield QED in the Lagrangian Formulation of General Superfield Theory of Fields  [PDF]
A. A. Reshetnyak
Physics , 2003,
Abstract: The basic theorem of the Lagrangian formulation for general superfield theory of fields (GSTF) is proved. The gauge transformations of general type (GTGT) and gauge algebra of generators of GTGT (GGTGT) as the consequences of the above theorem are studied. It is established the gauge algebra of GGTGT contains the one of generators of gauge transformations of special type (GGTST) as one's subalgebra. In the framework of Lagrangian formulation for GSTF the nontrivial superfield model generalizing the model of Quantum Electrodynamics and belonging to the class of gauge theory of general type (GThGT) with Abelian gauge algebra of GGTGT is constructed.
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