Since the quadrotor UAV can be considered as a rigid body aircraft, the analytic closed-form expressions of a rigid body's attitude kinematics are derived from differential of exponential on SO(3).
The condition of analytic solution is Rigid attachment condition, so in order to compare the numerical analytical solution with the same condition, k n, k s, T s, S s carried out the numerical analysis by setting unrealistic very large value.
The accuracy and the numerical properties of these schemes are evaluated with both continuous and discontinuous solutions in flows of rigid motion and incompressible deformation where analytic solutions are available.
At the core of our technique, we provide the analytic gradient of as-rigid-as-possible 2D transformations.
In order to simplify the analysis, pseudo-rigid-body model is transferred to the analytic equations of compliant mechanism.
Recently, a numerical inaccuracy trouble in the traditional semi-analytic method has been settled by the rigid body mode separation technique and high order approximation scheme.
In this paper, the semi-analytic design sensitivity of eigenvalues is obtained by the rigid body separation technique in reduced system.
The formulation derives from the analytic solution of two circular sheets externally clamped, with a central rigid core connecting them (representing the spot weld).
We conclude this section by an analytic derivation of the criterion for tilting for the case of long scaffolds that are very rigid relative to the membrane, and therefore are not deformed and attain their spontaneous curvature.
Overall, results showed that analytic models and FEA predictions lie within 10% of experimental data for the planar mechanism geometry in which pseudo rigid motion models apply.
