Since every kinematic trajectory is not always dynamically realizable for the spherical robot driven by two actuators, the mathematical model of the robot is derived based on the angular momentum conservation principle.
In this work, a novel moment-inversion algorithm, based on 1-D adaptive quadrature of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative quadrature weights).
Thus, thermodynamically consistent flux analysis can be performed on the resulting system without any additional considerations, and the behavior of the system is always physically realizable.
The full impact of this research may not always be immediately realizable or recognizable, but the contribution to our collective knowledge inspires further creativity and fosters the innovations of tomorrow.
Not only because that moment could vindicate American principles and mean a gain for American interests but because we claim those American principles to be universal principles - not realizable always or everywhere but to be approached when and where possible.
Finding multiple solutions to a multi-modal optimization problem is especially useful in engineering, as the best solution may not always be the best realizable due to various practical constraints.
However, we have recently shown that product in Eq. (2), or its reverse order, always leads to physically realizable Mueller matrix [ 33, 34].
However, critical examination shows that the derivation does not always lead to a physically realizable system, as each powertrain mount is not referenced to a single location.
But dreams always become more realistic and realizable when they are expressed.
Here Hcj can be arbitrarily selected without any limitation, and therefore one can always construct an acceleration Hamiltonian by only using realizable Hcj.
