this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. the specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. the basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...

Abstract An efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced. The method can be applied to nonintegrable equations as well as to integrable ones. Examples include multisoliton and periodic solutions of the famous integrable evolution equation (KdV) and the new solutions, describing interaction of solitary waves of nonintegr...

Abstract: Rijndael-The AES is 128-bit block cipher based on an elegant algebraic structure over F2. This cipher employs a simple approach to its substitution, permutation (SP) operations. We take a close look at its internals; the byte substitution transformation function is the only non-linear function in Rijndael The AES. This transformation comprises of two steps operating on each byte. Here...

The linearization problem of a second-order ordinary differential equation by the generalized Sundman transformation was considered earlier by Duarte, Moreira and Santos using the Laguerre form. The results obtained in the present paper demonstrate that their solution of the linearization problem for a second-order ordinary differential equation via the generalized Sundman transformation is not...

The Spring Loaded Inverted Pendulum (SLIP) has been extensively studied and used as an inspiration to research on legged locomotion. Biological data suggest that legs regulate energy production and removal via muscle activation, and therefore the conservative SLIP model cannot fully explain the robustness of many legged animals during running and hopping gaits. In this work we consider the acti...

The present paper addresses the use of high level languages, symbolic mathematical tools and code generation in an implementation of the finite element method, using a nonlinear hyperelasticity equation as example. Advantages of the software development method that will be demonstrated include closeness to the mathematics, enabling high human efficiency with easy to use high level languages, wh...