Circuit-algebraic calculation of steady-state modes of electric networks

In iterative algorithms for calculating the steady-state modes of AC electrical networks, it is proposed to use compact symbolic-numerical functions of nodal voltages formed by the method of circuit determinants once. These functions, due to algebraic convolution, have many times less complexity than the expanded expressions obtained by the tree method. Such functions are found by circuit-algebraic formulas in the form of a ratio of circuit determinants by allocating parameters. First of all, the conductivities (resistances) composed of a larger number of parallel (sequential) branches and incident nodes with a minimum (maximum) degree are distinguished. The original and derived schemes are recursively divided into parts that are similar in complexity. It is shown that the known computer systems for analytical calculations do not take into account the features of electrical circuits, without providing compact convolution.

Application of Integral Calculus in Kinematics

Kinematics is the study of the motion of mechanical points, bodies and systems without consideration of their associated physical properties and the forces acting on them. The study is often referred to as the geometry of motion, and it models these motions mathematically using algebra. The systems in kinematics are modeled to calculate such things as speeds and ratios. Kinematics is very useful in the conceptual design of mechanical systems. Initial geometries and velocities of bodies are a part of the model. While kinematics can help determine whether a design is theoretically possible, there are more complexities when designing something for the real world. Without consideration of materials, and the forces acting upon them, many theoretically possible designs would be prone to failure. Kinetics, in contrast to kinematics, does consider physical properties such as the mass of the bodies or the forces driving them. Kinetics is logically deduced from kinematics by way of algebraic calculation of physical properties and forces. Kinetics takes into account physical forces and properties including material properties, like mass rigidity, and tensile or compressive strength.