This paper presents an original undergraduate student project in theoretical mechanics: a demonstration of theory and experiment agreement inspired by a recently theoretically treated mechanical problem of coupled rolling motion of two cylinders. The problem of a mechanical system subjected to nonholonomic constraints is theoretically and numerically solved. Subsequently, the solution is quantitatively verified by a simple and inexpensive experiment, originally proposed and constructed by the authors. The comparison of results of the theoretical study with experimental output shows that there are instruments to directly verify rather abstract mathematical theories even on the undergraduate level. Moreover, combining the theoretical description of the problem with an appropriate laboratory experiment and computational procedures gives students a more complex view of the physical problem as a whole. This paper can be used by physics teachers on the undergraduate university level as an inspiration for an interesting student project. Moreover, the theoretical part of this paper itself can be used by interested intermediate students themselves as a good exercise in theoretical mechanics.
In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a general coupled rolling motion. Two goals are stressed.The first of them lies in the solution of an originally formulated problem of rolling motion of two rigid cylindrical bodies in the homogeneous gravitational field leading typically to nonlinear equations of motion. A solid cylinder can roll inside a ring under the static frictional force assuring rolling without slipping, the ring rolls again without slipping along a generally shaped terrain formed by hills and valleys. "Surprising behaviour" of the mechanical system which permits interesting applications is studied and discussed.The second purpose of the paper is to show that the geometrical theory of nonholonomic constrained systems on fibered manifolds proposed and developed in the last decade by Krupková and others is an effective tool for solving nonholonomic mechanical problems. A comparison of this method to alternative methods is given and the benefits of coordinate-free formulation are mentioned.In this paper, the geometrical theory is applied to the above mentioned mechanical problem. Both types of equations of motion resulting from the theory -deformed equations with the so called Chetaev type constraint forces containing Lagrange multipliers, and reduced equations free from multipliers -are found and discussed. Numerical solutions for two particular cases of the motion of the cylindrical system along a cylindrical surface are presented.
This paper enlarges the reservoir of solved tutor problems in non-holonomic mechanics at the undergraduate level of physics education. Unlike other, rather artificial, solved problems typically used, the streetboard-rider locomotion problem presented here represents an appealing contemporary real-world problem with interesting applications in a popular sport and in robotics. In this paper, the streetboard motion is discussed from the physical point of view. We show that the interesting snake-like motion performed by streetboard riders stems from its non-holonomic nature. The related non-holonomic constraints are derived and the problem of the mechanical system subjected to these non-holonomic constraints is solved using methods appropriate to the undergraduate university level. The analytical solution for the circular motion and the numerical solution for the general motion are obtained, the physical meaning of the derived constrained forces is investigated and the results are discussed with respect to observed streetboard-rider locomotion. The brief outline of the paper can be used as a demonstration example in non-holonomic mechanics lessons, while the paper itself establishes an original undergraduate computational student project in theoretical mechanics.
After the recent financial crisis the need for unchallenged tools evaluating the financial health of enterprises has even arisen. Apart from well-known techniques such as Z-score and logit models, a new approaches were suggested, namely the data envelopment analysis (DEA) reformulation for bankruptcy prediction and production function-based economic performance evaluation (PFEP). Being recently suggested, these techniques have not yet been validated for common use in financial sector, although as for DEA approach some introductory studies are available for manufacturing and IT industry. In this contribution we focus on the thorough validation calculations that evaluate these techniques for the specific agribusiness industry. To keep the data as homogeneous as possible we limit the choice of agribusiness companies onto the area of the countries of Visegrad Group. The extensive data set covering several hundreds of enterprises were collected employing the database Amadeus of Bureau van Dijk. We present the validation results for each of the four mentioned methods, outline the strengths and weaknesses of each approach and discuss the valid suggestions for the effective detection of financial problems in the specific branch of agribusiness.
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