Total capacitance

Capacitors connected in series

Capacitance C is a one of basic parameters of electric circuits next to resistance R and inductivity L. Capacitance C is defined as relation of charge Q to voltage V → C=Q/V. The measurement unit of capacitance is Farad → [C]=1F, Farad is a derived unit of SI system. Sometimes it is essential to calculate capacitance of electrical circuit which contains a few capacitors in its topology, therefore, it is often said that total capacitance of electrical circuit is computed. Sometimes during circuits analysis a subject is to calculate the total capacitance which is seen from specific circuit’s terminals.

Total capacitance

Nodal analysis

Nodal analysis

Nodal analysis is one of methods used for electrical networks analysis. Nodal analysis is based on Kirchhoff’s current law. Main idea of this method is to calculate electrical potentials of every node. This will allow to calculate voltages in branches since voltage is a difference of potentials. This approach has one rule which requires to assume that potential of one chosen node has be equal zero volts. Symbolically this chosen node is connected to the ground on electrical diagram.

Node voltage method

Dynamics of robot

Dynamics of robot

During robot’s motion various kinds of torques and forces works on robot. Some components of load is worn by robot’s construction. Rest of loads have to be equivalent by robot’s drives. If we construct a robot we have to know values of forces and torques because that knowledge is a base information for servodrives control. In this project dynamic forces and torques will be calculated for considered robot.

robot dynamics – project 1

Equilibrium equations

Static equilibrium equations

Beam is hanged to the ceiling via two ropes. Masses of ropes are so small that it is possible to omit them in computation. Beam has mass m[kg]. Force F[N] is placed in specified beam’s point. Static equilibrium equations for system have to be calculated. Reaction forces in ropes also have to be calculated. Beam is in gravity field. Beam has length 8·a. Gravity force which works on beam has to be placed in beam’s gravity center C.

static equilibrium equations example 3

Oblique throw – motion equation

Oblique throw - motion equation

Material point is thrown with start velocity v0. Between ground plane and vector of velocity v0 is an angle α. Material point is inside gravity field described by gravity acceleration g. Vector of gravity acceleration g is perpendicular to ground plane. It is assumed that move takes place in vacuum. It means that there is no air resist. Subject of example is to find equation of trajectory and value of angle which will provide maximal range of throw.

Oblique throw of material point

Physical pendulum

physical pendulum - motion equation

Physical pendulum is built with rigid body. One of rigid body ends is fixed to the ceiling. Rigid body is able to rotate around axis which is placed exactly in place where rigid’s end is fixed. Rotation axis is perpendicular to the plane of drawing. Rigid body has mass m and inertia I. Rigid body length is 2∙l. Note that inertia I is known for axis of rotations. If physical pendulum is in equilibrium position then it is not moving. In equilibrium position gravity force is balanced by rigid body’s reaction force. In a certain moment pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Pendulum is under gravity field, so gravity force works on it. Remember that physical pendulum is rigid body so gravity force is placed on rigid body’s gravity center C.

Physical pendulum – motion equation

Superposition method – currents calculation in electrical circuit

Electrical DC circuit - superposition method example 1.

Application of superposition method for simple electrical circuit. Electrical circuit is built from one voltage source and one current source. Main circuit will be divided into two sub-circuits because there are two sources. In the first sub-circuit current source will be the only extortion. In the second sub-circuit voltage source will be the only extortion.

Superposition method in electrical circuit – example 1

Mathematical pendulum

mathematical pendulum - motion equation

Mathematical pendulum is built with massless rope with length l. One of rope’s ends is fixed to the ceiling. To the second end of rope is fixed to the material point with mass m. Material point is then hanged to the rope. When mathematical pendulum is in equilibrium material point is not moving. In equilibrium position gravity force is balanced by rope’s tension force. In a certain moment mathematical pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Mathematical pendulum is under gravity field, so gravity force works on it.

Mathematical pendulum – motion equation

State space representation

state space representation - RLC circuit example 1.
In control theory and automation engineering dynamic models of system which are often created. It is a lot of cheaper and faster to simulate something than prepare real experiment. To simulate an object behaviour the state space representation is applied. State space representation allows to examine object features when it is under influence of various extortions. Set of examples about mentioned method are placed below.

State space representation for various systems