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Spinning rough disc moving in a rarefied medium

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from nonelastic interaction of gas particles with the body. We p...

On the two-dimensional rotational body of maximal Newtonian resistance

We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that the bodies are moving forward and at the same time slowly rotating. A two-dimensional geometric shape that confers to the body a resistance very close to the theoretical supremum value is obtained, which improves previous results.

Computing ODE symmetries as abnormal variational symmetries

We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 387 409], and is based on...

Two-dimensional body of maximum mean resistance

A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, [Alexander Yu. Plakhov, Paulo D.F. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271–2287], shapes of nonconvex bodies were sought which would maximize the ...

Reflection of parallel rays by a two-dimensional body of nearly maximal resistance

This Demonstration shows a class of nonconvex bodies that maximize resistance as they move forward while slowly rotating through a rarefied medium. This class of shapes yields a resistance very close to the theoretical maximum, improving all previous results found by the authors.

A double parabola with retroreflection properties

This Demonstration shows the reflective behavior of a two-dimensional shape formed by similar arcs of two parabolas. An interesting and unexpected reflective behavior arises when this shape takes a specific configuration, with two parabolas of unit focal length. In this particular configuration it is found that, except for the rays with absolute value of the entry angle less than 19.47º, a ray emerges from the ...

Computing ODE symmetries as abnormal variational symmetries

Computer Application ; We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 3...

Computação de simetrias variacionais e optimização da resistência aerodinâmica ...

Neste trabalho exploram-se alguns dos actuais recursos de computação científica no contexto da optimização estática e dinâmica. Começa-se por propor um conjunto de procedimentos computacionais algébricos que permitem automatizar todo o processo de obtenção de simetrias e leis de conservação, quer no contexto clássico do cálculo das variações, quer no contexto mais abrangente do controlo óptimo. A utilidade do p...

Uma forma bidimensional que maximiza a resistência aerodinâmica newtoniana

Um corpo bidimensional, apresentando um ligeiro movimento rotacional, desloca-se num meio rarefeito de partículas que colidem com ele de uma forma perfeitamente elástica. Em investigações que os dois primeiros autores realizaram anteriormente [Plakhov and Gouveia, 2007], procuraram-se formas de corpos que maximizassem a força de travagem do meio ao seu movimento. Dando continuidade a esse estudo, encetam-se ago...

Computing ODE symmetries from a variational point of view