Simulation of dynamic pinion course using Runge-Kutta's method and impact modeling

Once defined the relationship between the Starter Motor components and their functions, it is possible to develop a mathematical model capable to predict the Starter behavior during operation. One important aspect is the engagement system behavior. The development of a mathematical tool capable of predicting it is a valuable step in order to reduce the design time, cost and engineering efforts. A mathematical model, represented by differential equations, can be developed using physics laws, evaluating force balance and energy flow through the systems degrees of freedom. Another important physical aspect to be considered in this modeling is the impact conditions (particularly on the pinion and ring-gear contact). This work is a report of those equations application on available mathematical software and the resolution of those equations by Runge-Kutta's numerical integration method, in order to build an accessible engineering tool. Copyright © 2011 SAE International.

Mutual coupling modeling in transmission lines directly in the phase domain

This paper describes a computational model based on lumped elements for the mutual coupling between phases in three-phase transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile of the currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases. © 2011 IEEE.

Spin stabilized satellite's attitude analytical prediction

An analytical approach for spin stabilized attitude propagation is presented, considering the coupled effect of the aerodynamic torque and the gravity gradient torque. A spherical coordination system fixed in the satellite is used to locate the satellite spin axis in relation to the terrestrial equatorial system. The spin axis direction is specified by its right ascension and the declination angles and the equation of motion are described by these two angles and the magnitude of the spin velocity. An analytical averaging method is applied to obtain the mean torques over an orbital period. To compute the average components of both aerodynamic torque and the gravity gradient torque in the satellite body frame reference system, an average time in the fast varying orbit element, the mean anomaly, is utilized. Afterwards, the inclusion of such torques on the rotational motion differential equations of spin stabilized satellites yields conditions to derive an analytical solution. The pointing deviation evolution, that is, the deviation between the actual spin axis and the computed spin axis, is also availed. In order to validate the analytical approach, the theory developed has been applied for spin stabilized Brazilian satellite SCD1, which are quite appropriated for verification and comparison of the data generated and processed by the Satellite Control Center of the Brazil National Research Institute (INPE). Numerical simulations performed with data of Brazilian Satellite SCD1 show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of the Brazilian Research Institute.

Development of a simplified transmission line model directly in the phase domain

A transmission line digital model is developed direct in the phase and time domains. The successive modal transformations considered in the three-phase representation are simplified and then the proposed model can be easily applied to several operation condition based only on the previous knowing of the line parameters, without a thorough theoretical knowledge of modal analysis. The proposed model is also developed based on lumped elements, providing a complete current and voltage profile at any point of the transmission system. This model makes possible the modeling of non-linear power devices and electromagnetic phenomena along the transmission line using simple electric circuit components, representing a great advantage when compared to several models based on distributed parameters and inverse transforms. In addition, an efficient integration method is proposed to solve the system of differential equations resulted from the line modeling by lumped elements, thereby making possible simulations of transient and steady state using a wide and constant integration step. © 2012 IEEE.

On Non-ideal and Chaotic Energy Harvester Behavior

In this paper, we deal with the research of a proposed mathematical model of energy harvesting, including nonlinearities in the piezoelectric coupling and a non-ideal force of excitation. We showed using numerical simulations to analysis of the dynamic responses that, the power harvested was influenced by the nonlinear vibrations of the structure, as well as by the influence of the non-linearities in the piezoelectric coupling. We concluded through of the numerical results that the limited energy source was interacting with the system. Thus, the increasing of the voltage in DC motor led the system produce a good power response, especially in high-energy orbits in the resonance region, but the Sommerfeld effect occurs in the system and a chaotic behavior was found in the post-resonance region. So the power harvested along the time decreases because occurs loses of energy due the interaction between energy source and structure. Keeping the energy harvested constant over time is essential to make possible the use of energy harvesting systems in real applications. To achieve this objective, we applied a control technique in order to stabilize the chaotic system in a periodic stable orbit. We announced that the results were satisfactory and the control maintained the system in a stable condition. © 2012 Foundation for Scientific Research and Technological Innovation.

On the Chaotic Suppression of Both Ideal and Non-ideal Duffing Based Vibrating Systems, Using a Magnetorheological Damper

In this paper the dynamics of the ideal and non-ideal Duffing oscillator with chaotic behavior is considered. In order to suppress the chaotic behavior and to control the system, a control signal is introduced in the system dynamics. The control strategy involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system in a periodic orbit, obtained by the harmonic balance method, and a state feedback control, obtained by the state dependent Riccati equation, to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magnetorheological damper to actuate on the system. The control force of the damper is a function of the electric current applied in the coil of the damper, that is based on the force given by the controller and on the velocity of the damper piston displacement. Numerical simulations demonstrate the effectiveness of the control strategy in leading the system from any initial condition to a desired orbit, and considering the mathematical model of the damper (MR), it was possible to control the force of the shock absorber (MR), by controlling the applied electric current in the coils of the damper. © 2012 Foundation for Scientific Research and Technological Innovation.

Equivalent representation of mutual coupling in transmission lines by discrete element

This paper describes a computational model based on lumped elements for the mutual coupling between phases in transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile ofthe currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases. © 2003-2012 IEEE.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Modelagem matemática em câncer: dinâmica angiogênica e quimioterapia anti-neoplásica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equações diferenciais com retardo em biologia de populações: Renato Mendes Coutinho. -

Pós-graduação em Física - IFT

Análise numérica de condensadores do tipo arame-sobre-tubo usados em refrigeradores domésticos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propagação da atitude de satélites artificiais estabilizados por rotação: torque residual médio com o modelo de quadripolo para o campo geomagnético

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Modelagem do escoamento transiente ao longo de trocadores de calor tubo capilar-linha de sucção

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um olhar sobre as contribuições do professor Nelson Onuchic para o desenvolvimento da matemática no Brasil

Pós-graduação em Educação Matemática - IGCE

A influência de uma ação impulsiva no comportamento de soluções de equações diferenciais

Pós-graduação em Matemática Universitária - IGCE