Linear systemIn systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications.
Homogeneous functionFunction with a multiplicative scaling behaviourIn mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree.Linear functionIn mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero (a constant polynomial) or one (a linear polynomial). For distinguishing such a linear function from the other concept, the term affine function is often used.Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
Additive mapIn algebra, an additive map or additive function is a functionf{\displaystyle f} that preserves the addition operation: f(x+y)=f(x)+f(y){\displaystyle f(x+y)=f(x)+f(y)} for every pair of elements x{\displaystyle x} and y{\displaystyle y} in the domain of f{\displaystyle f}. For example, any linear map is additive. When the domain is the integers (ℤ), this is called a Z{\displaystyle \mathbb {Z} }-linear map.
Scalar (mathematics)In mathematics, more specifically in linear algebra, a scalar is an element of a field which is used to define a vector space through the operation of scalar multiplication: a vector (denoted v) multiplied by a scalar (denoted a) produces another vector (av). Real numbers and complex numbers may be used as scalars in real and complex vector spaces, respectively.
Deflection (engineering)In structural engineering, deflection is the degree to which a part of a long structural element (such as beam) is deformed laterally (in the direction transverse to its longitudinal axis) under a load. It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement). A longitudinal deformation (in the direction of the axis) is called elongation.PhysicsPhysics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. It is one of the most fundamental scientific disciplines. A scientist who specializes in the field of physics is called a physicist. Physics is one of the oldest academic disciplines.
EngineeringEngineering is the practice of systematically applying natural science and mathematics to design and improve systems, devices, or processes that solve problems under constraints. It is typically motivated by satisfying human needs, resulting in creations such as bridges, engines, smartphones, pacemakers, the internet, spacecraft, and washing machines.Structural loadA structural load or structural action is a mechanical load (more generally a force) applied to structural elements. A load causes stress, deformation, displacement or acceleration in a structure. Structural analysis, a discipline in engineering, analyzes the effects of loads on structures and structural elements. Excess load may cause structural failure, so this should be considered and controlled during the design of a structure.
Beam (structure)A beam is a structural element designed to carry loads perpendicular to its long (or "horizontal") axis. This contrasts with a strut or column, which bears its load perpendicular to its short (or "vertical") axis. A beam's mode of deflection is primarily by bending, as loads produce reaction forces at the beam's support points and internal bending moments, shear, stresses, strains, and deflections.
Frequency domainIn mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. While a time-domain graph shows how a signal changes over time, a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies.
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