The paper concludes with a brief discussion of applications where higher derivatives are relevant. These are the kinematic analysis and determination of motion spaces of serial mechanisms, the higher-order mobility analysis, and the algebraic formulation of motion equations....
Pinocchioexploits, at best, the sparsity induced by the kinematic tree of robotics systems. Thanks to modern programming language paradigms,Pinocchiocan unroll most of the computations directly at compile time, allowing to achieve impressive performances for an extensive range of robots, as illustrated ...
This transforms the original partial differential equation into a system of ordinary differential equations, which can often be solved exactly by analytical means. The superelements are usually n-sided polygons (or polyhedra, in the three-dimensional case) where the scaling direction (the non-...
Section 3 introduces the MMG model and the maneuvering equations of the vessel. The definition of the PMM captive tests is given in section 4. Section 5 presents the corresponding numerical methods. This is followed by a numerical analysis of the static drift and the dynamic PMM simulations, ...
Let us stress that, if we had not gone through the argument for NSNS- and RR-flux separately, the kinematic constraints arising in the reduction would have been totally obscure in the non-MUV sector. While it will generically be hard to identify δ1 explicitly, reducing t18 should be ...
In general, one can take the time derivative of any physical or kinematic property expressed in the spatial description: Section 2.4 Solid Mechanics Part III Kelly 241 v grad t dt d Material Time Derivative (2.4.6) For example, the rate of change of the density ) , ( t x of ...
The harmonic motion in pitch defines the kinematic relations for the angle of attack, pitching angular velocity, and rate as (4) Substituting (4) into (3), the new equation is (5) The unsteady moment coefficient periodically varies with stable amplitude over several cycles, and the primary...
Tests consider computing the partial derivatives of inverse and forward dynamics for robots ranging from kinematic chains to humanoids and quadrupeds. Compared to the previous open-source Pinocchio implementation, our analytical results uncover a key computational restructuring that enables efficiency gains. ...
This is done by introducing a Taylor series into the free undamped kinematic nonlinear equations of motion. Also, the approximate governing equations are improved by introducing a novel geometric restriction. By way of an example, it is shown that only the modal derivatives determined from the ...
To present the applications of the results, three problems are investigated in the field of satellite geodesy. In the first application, orbit propagated by the numerical solution of orbital equations is compared with the Keplerian motion. It is shown that the new method for solving ordinary ...