Inertia

About: Inertia is a research topic. Over the lifetime, 12006 publications have been published within this topic receiving 164291 citations.

The Dynamics of a Current Collection System for an Electric Locomotive

Abstract: The motion of an overhead trolley wire, suspended at equal intervals by stiff springs, in response to a pantograph moving with constant speed is analysed. The pantograph is modelled by two discrete masses connected by springs and dampers. Away from the supports the inertia and elasticity of the pantograph can be neglected and a simple solution for the wire and pantograph displacement is obtained. Near a support this solution is not valid as it predicts discontinuities in the vertical pantograph velocity. A different first approximation is then required in which the support elasticity and the pantograph inertia and elasticity must be included. This problem is reduced to that of solving a system of four linear differential equations containing one term with a stretched argument. The numerical and asymptotic solution of such a system is discussed and results are obtained for the contact force and pantograph displacement near a support in typical operating conditions. This disturbance at the support is propagated with the wire wave speed and reflected at the subsequent support, thus interacting with the pantograph again. This interaction is analysed and a uniformly valid solution obtained for the contact force over a complete span. Some conclusions are made about possible operating conditions in which loss of contact between the pantograph and the wire may occur.

Virtual Inertia: Current Trends and Future Directions

Abstract: The modern power system is progressing from a synchronous machine-based system towards an inverter-dominated system, with large-scale penetration of renewable energy sources (RESs) like wind and photovoltaics. RES units today represent a major share of the generation, and the traditional approach of integrating them as grid following units can lead to frequency instability. Many researchers have pointed towards using inverters with virtual inertia control algorithms so that they appear as synchronous generators to the grid, maintaining and enhancing system stability. This paper presents a literature review of the current state-of-the-art of virtual inertia implementation techniques, and explores potential research directions and challenges. The major virtual inertia topologies are compared and classified. Through literature review and simulations of some selected topologies it has been shown that similar inertial response can be achieved by relating the parameters of these topologies through time constants and inertia constants, although the exact frequency dynamics may vary slightly. The suitability of a topology depends on system control architecture and desired level of detail in replication of the dynamics of synchronous generators. A discussion on the challenges and research directions points out several research needs, especially for systems level integration of virtual inertia systems.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory

Abstract: The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.

Centroidal dynamics of a humanoid robot

Abstract: The center of mass (CoM) of a humanoid robot occupies a special place in its dynamics. As the location of its effective total mass, and consequently, the point of resultant action of gravity, the CoM is also the point where the robot's aggregate linear momentum and angular momentum are naturally defined. The overarching purpose of this paper is to refocus our attention to centroidal dynamics: the dynamics of a humanoid robot projected at its CoM. In this paper we specifically study the properties, structure and computation schemes for the centroidal momentum matrix (CMM), which projects the generalized velocities of a humanoid robot to its spatial centroidal momentum. Through a transformation diagram we graphically show the relationship between this matrix and the well-known joint-space inertia matrix. We also introduce the new concept of "average spatial velocity" of the humanoid that encompasses both linear and angular components and results in a novel decomposition of the kinetic energy. Further, we develop a very efficient $$O(N)$$ O ( N ) algorithm, expressed in a compact form using spatial notation, for computing the CMM, centroidal momentum, centroidal inertia, and average spatial velocity. Finally, as a practical use of centroidal dynamics we show that a momentum-based balance controller that directly employs the CMM can significantly reduce unnecessary trunk bending during balance maintenance against external disturbance.