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

→ secretary-general.

→ general; → secretary.

The act or process of generalizing; → generalize.
A result of this process; a general statement, proposition, or principle.

Verbal noun of → generalize.

To make general, to include under a general term; to reduce to a general form.
To infer or form a general principle, opinion, conclusion, etc. from only a few facts, examples, or the like.

→ general; → -ize.

Made general. → generalized coordinates; → generalized velocities.

P.p. of → generalize

In a material system, the independent parameters which completely specify the configuration of the system, i.e. the position of its particles with respect to the frame of reference. Usually each coordinate is designated by the letter q with a numerical subscript. A set of generalized coordinates would be written as q₁, q₂, ..., q_n. Thus a particle moving in a plane may be described by two coordinates q₁, q₂, which may in special cases be the → Cartesian coordinates x, y, or the → polar coordinates r, θ, or any other suitable pair of coordinates. A particle moving in a space is located by three coordinates, which may be Cartesian coordinates x, y, z, or → spherical coordinates r, θ, φ, or in general q₁, q₂, q₃. The generalized coordinates are normally a "minimal set" of coordinates. For example, in Cartesian coordinates the simple pendulum requires two coordinates (x and y), but in polar coordinates only one coordinate (θ) is required. So θ is the appropriate generalized coordinate for the pendulum problem.

→ generalized; → coordinate.

In → Lagrangian dynamics, forces related to → generalized coordinates. For any system with n generalized coordinates q_i (i = 1, ..., n), generalized forces are expressed by F_i = ∂L/∂q_i, where L is the → Lagrangian function.

→ generalized; → force.

In → Lagrangian dynamics, momenta related to → generalized coordinates. For any system with n generalized coordinates q_i (i = 1, ..., n), generalized momenta are expressed by p_i = ∂L/∂q^._i, where L is the → Lagrangian function.

→ generalized; → momentum.

The time → derivatives of the → generalized coordinates of a system.

→ generalized; → velocity.

To bring into existence; create; produce.
Math.: To trace (a figure) by the motion of a point, straight line, or curve.

Generate, from M.E., from L. generatus "produce," p.p. of generare "to bring forth," from gener-, genus "descent, birth," akin to Pers. zâdan, Av. zan- "to give birth," as explained below.

Âzânidan, from â- nuance/strengthening prefix + zân, from Av. zan- "to bear, give birth to a child, be born," infinitive zazāite, zāta- "born;" Mod.Pers. zâdan, present stem zā- "to bring forth, give birth" (Mid.Pers. zâtan; cf. Skt. jan- "to produce, create; to be born," janati "begets, bears;" Gk. gignomai "to happen, become, be born;" L. gignere "to beget;" PIE base *gen- "to give birth, beget") + -idan infinitive suffix.

1) A coming into being.
2) The → production of → energy (→ heat or → electricity).

Verbal noun of → generate.

1) Capable of producing or creating.
2) Pertaining to the production of offspring.

→ generate; → -ive.

1) A machine for converting one form of energy into another.
2) Geometry: That which creates a line, a surface, a solid by its motion.

From L. generator "producer," from genera(re)→ generate + -tor a suffix forming personal agent nouns from verbs and, less commonly, from nouns.

Âzângar, from âzân the stem of âzânidan→ generate + -gar suffix of agent nouns, from kar-, kardan "to do, to make" (Mid.Pers. kardan; O.Pers./Av. kar- "to do, make, build," Av. kərənaoiti "makes;" cf. Skt. kr- "to do, to make," krnoti "makes," karma "act, deed;" PIE base k^wer- "to do, to make").

Pertaining or according to → genetics or → genes.

From Gk. genetikos, from genesis "origin," → gene; → -ic.

The study of heredity and inheritance, of the transmission of traits from one individual to another, of how genes are transmitted from generation to generation.

From → genetic and → -ics.

The quality or state of being → heterogeneous. See also → homogeneity, → inhomogeneity.

Noun from → heterogeneous.

1) Composed of parts of different kinds; having widely dissimilar elements or constituents. See also → homogeneous, → inhomogeneous.
2) Chemistry: A mixture that does not have uniform composition and properties throughout; composed of different substances or the same substance in different phases.

→ hetero- + -genous, → homogeneous.

State or quality of having a uniform appearance or composition, being homogeneous

→ homogeneous + → -ity.

1) Of uniform composition or having a common property throughout.
2) Math.: Of the same kind so as to be commensurable. Of the same degree or dimension. → anisotropic homogeneous cosmological model, → homogeneous fluid, → homogeneous linear differential equation, → homogeneous Universe, → homogeneous turbulence, → inhomogeneous, → nonhomogeneous, → nonhomogeneous linear differential equation.

Homogeneous, from M.L. homogeneus, from Gk. homogenes "of the same kind," from homos "same," → homo-, + genos "race, kind," gonos "birth, offspring," from PIE base *gen-/*gon-/*gn- "to produce, beget, be born," cf. Av. zan- "to bear, give birth to a child, be born," infinitive zazāite, zāta- "born," zana- "race" (in sruuô.zana- "belonging to the race of the horned ones"), O.Pers. zana- "tribe" (in paru-zana- "consisting of many tribes"), Skt. janati "begets, bears," jana- "creature, human being, race, tribe, people;" L. genus "race, stock, kind," gignere "to beget."

Hamgen "of the same kind, like each other; friend, partner," from ham-, → homo-, + gen "kind," O.Pers./Av. zana- "race; tribe," cognate with L. genus, as above). Alternatively, gen may be a variant of Mid./Mod.Pers. gôn/gun "kind, type; manner; color, skin color," from Av. gaona- "hair, hair color, color."

A fluid with uniform properties throughout, but meteorologists sometimes designate as homogeneous a fluid with constant density.

→ homogeneous, → fluid.

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

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