An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

Lying on the same straight line. Collinear points are a set of points on the same line.

→ com- + → linear.

A system of two or more forces that lie along the same → line of action.

→ collinear; → force.

A mathematical property where all points lying on a line initially still lie on a line after transformation.

→ collinear; → -ity.

Consisting of, represented by, or bound by curved lines. → rectilinear.

From → curve + → linear.

A → linear differential equation if the right-hand member is zero, Q(x) = 0, on interval I.

→ homogeneous; → linear; → differential; → equation.

Confined to first-degree algebraic terms in the relevant variables.

Adj. of → line.

The rate of change of the → linear velocity with time. It is defined by the expression Δv/Δt and is equal to the → first derivative of the → linear velocity.

→ linear; → acceleration.

Taking the first term in the Taylor series as an approximation to a mathematical function at a given point. → first approximation.

→ linear; → approximation.

A version of → planispheric astrolabe in which the → celestial sphere and the various circles of altitude and declination are projected on to a line represented by a staff. The staff is equivalent to the meridian line and contains markings to indicate the centers of these circles and their intersections with the meridian. By attaching three ropes to the appropriate points on the staff to act as radii, the circles and their intersections can be reconstructed. One of the ropes was attached to a plumb line. A scale giving chord lengths in the meridian circle extended the linear astrolabe's range of applications. It was invented by the Iranian mathematician and astronomer Sharafeddin Tusi (c1135-1213), but no early example has survived. Same as → Sharafeddin's staff and Tusi's staff.

→ linear; → astrolabe.

A measure of how well data points fit a straight line. When all the points fall on the line it is called a perfect correlation. When the points are scattered all over the graph there is no correlation.

→ linear; → correlation.

The real physical diameter, as opposed to angular diameter.

→ linear; → diameter.

An equation in which the → dependent variable y and all its differential coefficients occur only in the first degree. A linear differential equation of → order  order n has the form:
f_n(x)y⁽ⁿ⁾ + f_n-1(x)y^(n-1) + ... + f₁(x)y^' + f₀(x)y = Q(x),
where f₀(x), f₁(x), ..., f_n(x) and Q(x) are each continuous functions of x defined on a common interval I and f_n(x)≠ 0 in I. A linear differential equation cannot have, for example, terms such as y² or (y^')^1/2. See also: → homogeneous linear differential equation; → nonhomogeneous linear differential equation.

→ linear; → differential; → equation.

A system of three charges +q, -2q, and +q, arranged along a line to form an axial quadrupole. The → electric potential  V due to a linear quadrupole varies as 1/r³, whereas the → electric intensity  E varies as 1/r⁴.

→ linear; → electric; → quadrupole.

An equation composed of first degree variables and representing a straight line.

→ linear; → equation.

A function expressed by a → first degree equation that can be graphically represented in the → Cartesian coordinate plane by a → straight line.

→ linear; → function.

An instability that can be described (to first-order accuracy) by linear (or tangent linear) equations.

→ linear; → instability.

The product of an object's → mass and → velocity. It is a → vector and points in the same direction as the velocity vector. Linear momentum is distinguished from → angular momentum. When there is no opportunity for confusion, usually the term momentum is used instead of linear momentum.

→ linear; → momentum.

Assumption that the variations in the plasma parameters, due to the presence of waves, are small (to the first order) as compared to the undisturbed parameters. This makes it possible to linearize equations by dropping out second order (and higher) nonlinear terms.

→ linear; → perturbation; → theory.

Of an electromagnetic radiation, a → polarization in which the electric vibrations are confined to one plane along the direction of propagation. Also called → plane polarization. See also → circular polarization.

→ linear; → polarization.

A procedure for finding the maximum or minimum of a → linear function where the → arguments are subject to linear → constraints. For problems involving more than two variables or problems involving a large number of constraints, solution methods used are those that are adaptable to computers. A well-known such → algorithm is the → simplex method.

→ linear; → programmings.