Vaidya Spacetime in Brans-Dicke Gravity's Rainbow

In this note we study an energy dependent deformation of a time dependent geometry in the background of Brans-Dicke gravity theory. The study is performed using the gravity's rainbow formalism. We compute the field equations in Brans-Dicke gravity's rainbow using Vaidya metric which is a time dependent geometry. We study a star collapsing under such conditions. Our prime objective is to determine the nature of singularity formed as a result of gravitational collapse and its strength. The idea is to test the validity of the cosmic censorship hypothesis for our model. We have also studied the effect of such a deformation on the thermalization process. In this regard we have calculated the important thermodynamical quantities such as thermalization temperature, Helmholtz free energy, specific heat and analyzed the behavior of such quantities.Comment: 19 pages, 15 figure

Stability analysis of non-holonomic inverted pendulum system

The inverted pendulum is doubtlessly one of the most famous control problems found in most control text books and laboratories worldwide. This popularity comes from the fact that the inverted pendulum exhibits nonlinear, unstable and non-minimum phase dynamics. The basic control objective of the study is to design a controller in order to maintain the upright position of the pendulum while also controlling the position of the cart. In our study we explored the relationship that the tuning parameters (weight on the position of the car and the angle that the pendulum makes with the vertical) of a classical inverted pendulum on a cart has on the pole placement and hence on the stability of the system. We then present a family of curves showing the local root-locus and develop relationships between the weight changes and the system performance. We describe how these locus trends provide insight that is useful to the control designer during the effort to optimize the system performance. Finally, we use our general results to design an effective feedback controller for a new system with a longer pendulum, and present experiment results that demonstrate the effectiveness of our analysis. We then designed a simulation-based study to determine the stability characteristics of a holonomic inverted pendulum system. Here we decoupled the system using geometry as two independent one dimensional inverted pendulum and observed that the system can be stabilized using this method successfully with and without noise added to the system. Next, we designed a linear system for the highly complex inverted pendulum on a non-holonomic cart system. Overall, the findings will provide valuable input to the controller designers for a wide range of applications including tuning of the controller parameters to design of a linear controller for nonlinear systems

Correspondence between Electro-Magnetic Field and other Dark Energies in Non-linear Electrodynamics

In this work, we have considered the flat FRW model of the universe filled with electro-magnetic field. First, the Maxwell's electro-magnetic field in linear form has been discussed and after that the modified Lagrangian in non-linear form for accelerated universe has been considered. The corresponding energy density and pressure for non-linear electro-magnetic field have been calculated. We have found the condition such that the electro-magnetic field generates dark energy. The correspondence between the electro-magnetic field and the other dark energy candidates namely tachyonic field, DBI-essence, Chaplygin gas, hessence dark energy, k-essenece and dilaton dark energy have been investigated. We have also reconstructed the potential functions and the scalar fields in this scenario.Comment: 11 pages, 7 figure

Stability analysis of non-holonomic inverted pendulum system

The inverted pendulum is doubtlessly one of the most famous control problems found in most control text books and laboratories worldwide. This popularity comes from the fact that the inverted pendulum exhibits nonlinear, unstable and non-minimum phase dynamics. The basic control objective of the study is to design a controller in order to maintain the upright position of the pendulum while also controlling the position of the cart. In our study we explored the relationship that the tuning parameters (weight on the position of the car and the angle that the pendulum makes with the vertical) of a classical inverted pendulum on a cart has on the pole placement and hence on the stability of the system. We then present a family of curves showing the local root-locus and develop relationships between the weight changes and the system performance. We describe how these locus trends provide insight that is useful to the control designer during the effort to optimize the system performance. Finally, we use our general results to design an effective feedback controller for a new system with a longer pendulum, and present experiment results that demonstrate the effectiveness of our analysis. We then designed a simulation-based study to determine the stability characteristics of a holonomic inverted pendulum system. Here we decoupled the system using geometry as two independent one dimensional inverted pendulum and observed that the system can be stabilized using this method successfully with and without noise added to the system. Next, we designed a linear system for the highly complex inverted pendulum on a non-holonomic cart system. Overall, the findings will provide valuable input to the controller designers for a wide range of applications including tuning of the controller parameters to design of a linear controller for nonlinear systems

Stability analysis of non-holonomic inverted pendulum system

The inverted pendulum is doubtlessly one of the most famous control problems found in most control text books and laboratories worldwide. This popularity comes from the fact that the inverted pendulum exhibits nonlinear, unstable and non-minimum phase dynamics. The basic control objective of the study is to design a controller in order to maintain the upright position of the pendulum while also controlling the position of the cart. In our study we explored the relationship that the tuning parameters (weight on the position of the car and the angle that the pendulum makes with the vertical) of a classical inverted pendulum on a cart has on the pole placement and hence on the stability of the system. We then present a family of curves showing the local root-locus and develop relationships between the weight changes and the system performance. We describe how these locus trends provide insight that is useful to the control designer during the effort to optimize the system performance. Finally, we use our general results to design an effective feedback controller for a new system with a longer pendulum, and present experiment results that demonstrate the effectiveness of our analysis. We then designed a simulation-based study to determine the stability characteristics of a holonomic inverted pendulum system. Here we decoupled the system using geometry as two independent one dimensional inverted pendulum and observed that the system can be stabilized using this method successfully with and without noise added to the system. Next, we designed a linear system for the highly complex inverted pendulum on a non-holonomic cart system. Overall, the findings will provide valuable input to the controller designers for a wide range of applications including tuning of the controller parameters to design of a linear controller for nonlinear systems.</p