Dual-complex quaternion representation of gravitoelectromagnetism

In this paper, we propose the generalized description of electromagnetism and linear gravity based on the combined dual numbers and complex quaternion algebra. In this approach, the electromagnetic and gravitational fields can be considered as the components of one combined dual-complex quaternionic field. It is shown that all relations between potentials, field strengths and sources can be formulated in the form of compact quaternionic differential equations. The alternative reformulation of equations of gravitoelectromagnetism based on formalism of [Formula: see text] matrices is also discussed. The results reveal the similarity and isomorphism of distinctive algebraic structures.

Simulation of an Exoskeleton with a Hybrid Linear Gravity Compensator

Purpose of research. Development of a mathematical model of an exoskeleton equipped with a hybrid linear gravity compensator (HLGC), dynamic analysis on the example of a typical exoskeleton application scenario (in the process of lifting a load), obtaining time patterns of changes in system parameters, including electric drive torques allowing assessment of power plan power consumption and energy efficiency. The article deals with the challenging issue of improving the efficiency of the exoskeletal suit by means of HLGC. The use of a hybrid approach makes it possible to increase the efficiency of assisting the exoskeletal suit when performing various technological operations, for example, when lifting a load, when tilting and holding. Methods. When developing a mathematical model, an original approach was used to form the motion trajectory of the exoskeleton sectors during operation, based on the use of seventh-order polynomials. The paper uses a mathematical model represented by a system of second-order differential equations that connects the moments acting on the operator and the exoskeleton, the angular accelerations of the operator's back and the exoskeleton. Results. During numerical simulation, time diagrams of changes in system parameters, angles of rotation of exoskeleton hinges, moments that occur in a hybrid LGC, as well as graphs of current consumption of engines when performing lift and tilt with a load are obtained. Conclusion. In the course of the research, a kinematic model of an exoskeleton suit equipped with a GLGC was developed, second-order differential equations describing the dynamic behavior of the electromechanical system were written, and numerical simulation was performed to estimate the forces and energy consumption in the exoskeleton hinges and the drive of the hybrid linear gravity compensator.

Mixed Rossby–Gravity Wave–Wave Interactions

Mixed triad wave–wave interactions between Rossby and gravity waves are analytically derived using the kinetic equation for models of different complexity. Two examples are considered: initially vanishing linear gravity wave energy in the presence of a fully developed Rossby wave field and the reversed case of initially vanishing linear Rossby wave energy in the presence of a realistic gravity wave field. The kinetic equation in both cases is numerically evaluated, for which energy is conserved within numerical precision. The results are validated by a corresponding ensemble of numerical model simulations supporting the validity of the weak-interaction assumption necessary to derive the kinetic equation. Since they are generated by nonresonant interactions only, the energy transfers toward the respective linear wave mode with vanishing energy are small in both cases. The total generation of energy of the linear gravity wave mode in the first case scales to leading order as the square of the Rossby number in agreement with independent estimates from laboratory experiments, although a part of the linear gravity wave mode is slaved to the Rossby wave mode without wavelike temporal behavior.