The principle of virtual work states that if a body is in static and dynamic equilibrium, then the sum of all the virtual work done by all external forces and couple moments for any given virtual displacement must be zero.
In static equilibrium, a body can experience an imaginary or virtual movement, such as displacement or rotation. The virtual work done by a force is equal to the dot product of force and virtual displacement in the direction of the force. When it comes to virtually rotating a...

MATLAB stands for Matrix Laboratory. MathWorks developed MATLAB as a multi-paradigm numerical computing environment and proprietary programming language. It has evolved significantly over the years to become a tool utilized by engineers, scientists, and mathematicians for various tasks, including matrix calculations, developing algorithms, data analysis, and visualization. MATLAB's applications span various industries and disciplines. It's used in image and signal processing, communications,...

Econometric Views, often stylized as EViews, is a package that merges statistical analysis with econometric studies. It is designed to provide tools for time series analysis, forecasting, and econometric model simulation. The software originated from MicroTSP software and has evolved significantly since its inception in 1981. The history of EViews is marked by a continuous effort to enhance its computational speed and user interface. It was initially developed for large computing systems but...

The motion of a simple pendulum is governed by Newton’s Second Law in its rotational form, which relates the net torque on the bob to its angular acceleration. This physical law gives rise to a second-order differential equation in which the angular acceleration is proportional to the sine of the displacement angle.Because of the sin(𝜃) term, the governing equation is a nonlinear differential equation, which is difficult to solve analytically. To simplify the mathematical model, the sine...

Modern aerospace navigation depends on the accurate prediction of motion in three-dimensional space. In defense applications, radar systems continuously track both interceptors and moving aerial targets to find whether their flight paths will result in a collision. These motions are modeled mathematically as space curves, which represent paths that change continuously with time. Each object’s position is described by a vector function that specifies its location in terms of time-dependent...

Multiple integrals provide a powerful mathematical framework for calculating physical quantities distributed throughout two- and three-dimensional regions. One important application is the determination of volume in objects with curved geometries, such as storage tanks, pipes, and reservoirs. Cylindrical coordinates are especially useful for systems with rotational symmetry because they simplify the description of circular and paraboloid-shaped regions.Consider a paraboloid-shaped water tank...