## Appendix A Logistics and [PERSON]'s Principle of Least Action  
The science of analytical classical mechanics can be based on two different but mathematically equivalent principles: a differential principle, on the one hand, and an integral one, on the other hand. While the differential principle dates back to [PERSON], the second one dates back to [PERSON] and [PERSON]. [PERSON]'s, [PERSON]'s and [PERSON]'s equations of motion are extensively discussed in many textbooks on theoretical physics, such as those of [PERSON] and [PERSON] mentioned in references [23; 24]. In view of this fact, we limit  
Figure 13: Micro-inertial sensor for measuring linear and rotational motions of cars; (**a**) linear and rotational motions acting on a silicon proof mass; (**b**) micromachined interdigital capacitors for turning mechanical motions into electrical readout signals; (**c**) example of a micro inertial sensor system housed in a microelectronic chip package [25; 26; 27; 28; 29].  
ourselves here to a very brief discussion of those matters, aiming particularly at establishing a connection to the work discussed in the main text.  
The key idea underlying [PERSON]'s differential equations of motion is that a particle of mass \(M\), starting out at a spacetime location \(A(\overset{\rightarrow}{r}_{A},t_{A})\), where \(\overset{\rightarrow}{r}_{A}\) stands for the 3D position of the particle and \(t_{A}\) for time, does move through an external force field \(\phi(\overset{\rightarrow}{r},t)\) by locally and momentarily adjusting its mechanical momentum \(P(\overset{\rightarrow}{r},t)=Mv(\overset{\rightarrow}{r},t)\) to the field strength and field direction of \(\phi(\overset{\rightarrow}{r},t)\) at the respective space-time location \((\overset{\rightarrow}{r},t)\). As it is well known, [PERSON]'s equations of motions successfully describe the results of well-proven facts such as those that a stone released from the hand will fall in a straight line towards the ground and that the planets of the solar system are circulating around the sun in elliptic orbits.  
In the 17 th and 18 th century, the Newtonian picture of classical motion was refined and modified, particularly through the work of [PERSON] and [PERSON]. This later work yielded a very important result that the science of classical mechanics can also be based on an integral principle, which later became known as the \"Hamiltonian principle\" or \"Principle of least action\". Mathematically, this latter principle states that a particle moving through an external force field \(\phi(\overset{\rightarrow}{r},t)\) will follow its path from \(A\) to \(B\) along a trajectory \(\Gamma(\overset{\rightarrow}{r},t)\) that minimizes the action integral,  
\[W_{AB}\ =\int_{t_{A}}^{t_{B}}L(\overset{\rightarrow}{r},t)dt. \tag{1}\]  
In this equation, \(L(\overset{\rightarrow}{r},t)=T(\overset{\rightarrow}{r},t)-V(\overset{ \rightarrow}{r},t)\) is the Lagrangian function and \(T(\overset{\rightarrow}{r},t)\) and \(V(\overset{\rightarrow}{r},t)\) are the kinetic and potential energies of the moving particle at space-time positions \(\overset{\rightarrow}{r}\) and \(t\). Equation (1) mathematically represents a functional that maps an entire trajectory onto a single real number \(W_{AB}\), which turns it into an integral principle. The number \(W_{AB}\) takes the physical dimensions of \([energy\times time]\), a physical entity that was later termed in the English language as \"physical action\". In addition to appearing in the theory of classical mechanical motion and proving its use there, the concept of physical action had later also revealed to be useful in the development of the quantum theory (QM) of atoms and molecules and later also in the quantum field theory of photons and the electromagnetic interaction (QED).