rolling-based seismic isolation systems, in which rollers of circular or non-circular section are used, are less expensive and easier to manufacture. however, this type of isolation suffers from either lack of restoring or re-centering capability, or weakness against uplift forces. to resolve the first shortcoming the use of elliptical as well as pillow-shape rolling parts has been suggested, a...

the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

in this paper a new isolating system is introduced for short to mid-rise buildings. in comparison to conventional systems such as lrb and hrb, the proposed system has the advantage of no need to cutting edge technology and has low manufacturing cost. this system is made up of two orthogonal pairs of pillow-shaped rollers that are located between flat bed and plates. by using this system in two ...

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

In this survey we address the Björling problem for various classes of surfaces associated to the Euler–Lagrange equation of the Helfrich elastic energy subject to volume and area constraints.

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts (the Ricci tensor and the term proportional to the curvature scalar) with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, wit...