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

A function that describes the motion of a → dynamical system in terms of the → Lagrangian function, → generalized coordinates, → generalized momenta, and time. For a → holonomic system having n degrees of freedom, the Hamiltonian function is of the form: H = Σp_iq^._i - L(q_i,q^._i,t) (summed from i = 1 to n), where L is the Lagrangian function. If L does not depend explicitly on time, the system is said to be → conservative and H is the total energy of the system. The Hamiltonian function plays a major role in the study of mechanical systems. Also called → Hamiltonian.

Introduced in 1835 by the Irish mathematician and physicist William Rowan Hamilton (1805-1865); → function.

The dynamical operator in → quantum mechanics that corresponds to the → Hamiltonian function in classical mechanics.

→ Hamiltonian function; → operator.

A small → village.

M.E. hamlet, hamelet, from O.Fr. hamelet "small village," diminutive of O.Fr. hamel "village," itself diminutive of ham "village;" of Germanic origin; cf. E. home, O.E. ham, Du. heem, Ger. Heim; cognate with → city.

Kalâ, from Tabari kalâ "village, borough." Dozens of village names contain kalâ az suffix in Mâzandarân and Gilan.

1) The terminal part of the forelimb in humans and other primates.
2) A part serving the function of or resembling a hand.

M.E. O.E. hond, hand "hand; side; power;" cf. O.S., O.Fris., Du., Ger. hand, O.N. hönd, Goth. handus.

Dast "hand; strength; superiority;" Mid.Pers. dast; O.Pers. dasta-; Av. zasta-; cf. Skt. hásta-; Gk. kheir; L. praesto "at hand;" Arm. jern "hand;" Lith. pa-žastis "arm-pit;" PIE *ghes-to-.

A scholarly book on a specific subject that is conveniently handled.

→ hand; → book.

1) A tendency to use one hand rather than the other.
2) The property of an object (as a molecule) of not being identical with its mirror image. Same as → chirality (Merriam-Webster.com).
See also: → B-mode polarization, → E-mode polarization.

→ hand + -ed + → -ness.

Dastâli, from dast, → hand, + -al, → -al, + noun suffix -i, on the model of → chirality.

The → polarization arising from line scattering in the presence of "weak" magnetic fields. The effect occurs when precession around magnetic field depolarizes and rotates polarization of the scattered light. The Hanle effect is sensitive to ~10³ times smaller field strengths than the → Zeeman effect. It is in particular used to measure the weak magnetic field of the solar → prominences, which is 10^-3 tesla and over 10^-2 tesla for the active prominences.

Named for the German physicist Wilhelm Hanle (1901-1993), who published his his discovery in 1923 (Naturwissenschaften 11, 690); → effect.

Take place; occur; befall.

M.E. hap(pe)nen, from hap "luck, chance" + -en.

Fatidan, variant of oftâdan, fotâdan "to fall; to be fall, occur;" Sistani aft, aftid "to → fall."

An → event or occurrence.

Verbal noun of → happen; → -ing.

To disturb persistently; bother continually. → galaxy harassment.

From M.Fr. harasser "tire out, vex," possibly from O.Fr. harer "set a dog on," and perhaps blended with O.Fr. harier "to harry, draw, drag."

Sotuhidan, infinitive from sotuh, → harassed.

Subject to → harassment.

P.p. of → harass.

Sotuh "afflicted, distressed, helpless," from Mid.Pers. stô "distressed, defeated;" O.Pers. us-tav-, from us- "out, without," ultimately from *ustau- "unable, weak," from *us- "out," → ex-, + *tau- "to be able," → power.

The act or an instance of harassing. → galaxy harassment.

Verbal noun of → harass.

Not soft; severe.
Physics: Having relatively high energy (of a beam of particles or photons); → hard X-rays; opposed to → soft.

Hard, from O.E. heard "solid, firm; severe, rigorous," from P.Gmc. *kharthus (cf. Du. hard, O.H.G. harto "extremely, very," Goth. hardus "hard"), from PIE *kratus "power, strength" (cf. Gk. kratos "strength," kratys "strong").

Saxt "hard, strong, firm, secure, solid, vehement, intense," from Mid.Pers. saxt "hard, strong, severe;" Av. sak- "to understand or know a thing, to mark;" cf. Skt. śakta- "able, strong," śaknoti "he is strong," śiksati "he learns."

In → stellar dynamics studies of → three-body encounters, a → binary system whose → binding energy far exceeds the → kinetic energy of the relative motion of an incoming third body. In such an encounter, a hard binary is likely to get harder and transfer energy to the incoming star, whereas a → soft binary is likely to be disrupted.

→ hard; → binary.

The front, bony part of the roof of the mouth. → soft palate.

→ hard; → palate.

The short wavelength, high energy end of the → electromagnetic spectrum. Hard X-rays are typically those with energies greater than around 10 keV. The dividing line between hard and → soft X-rays is not well defined and can depend on the context.

→ hard; → X-rays.

Any physical equipment. The physical equipment comprising a computer system; opposed to → software.

→ hard + ware, from M.E., from O.E. waru, from P.Gmc. *waro (cf. Swed. vara, Dan. vare, M.Du. were, Du. waar, Ger. Ware "goods").

Saxt-afzâr, from saxt, → hard + afzâr "instrument, means, tool," from Mid.Pers. afzâr, abzâr, awzâr "instrument, means," Proto-Iranian *abi-cāra- or *upa-cāra-, from cāra-, cf. Av. cārā- "instrument, device, means" (Mid.Pers. câr, cârag "means, remedy;" loaned into Arm. aucar, aucan "instrument, remedy;" Mod.Pers. câré "remedy, cure, help"), from kar- "to do, make, build;" kərənaoiti "he makes" (Pers. kardan, kard- "to do, to make"); cf. Skt. kr- "to do, to make," krnoti "he makes, he does," karoti "he makes, he does," karma "act, deed;" PIE base k^wer- "to do, to make").

(adj.) Of, pertaining to, or noting a series of oscillations in which each oscillation has a frequency that is an integral multiple of the same basic frequency.
(n.) A wave motion, superimposed on a fundamental wave, having a frequency which is an integral multiple of the fundamental frequency. → overtone.

From L. harmonicus, from Gk. harmonikos "harmonic, musical," from harmonia "agreement, concord of sounds," related to harmos "joint," arariskein "to join together;" PIE base *ar- "to fit together."

Hamâhang, "harmonious, concordant," from ham- "together, with; same, equally, even" (Mid.Pers. ham-, like L. com- and Gk. syn- with neither of which it is cognate. O.Pers./Av. ham-; Skt. sam-; also O.Pers./Av. hama- "one and the same," Skt. sama-; Gk. homos-; originally identical with PIE numeral *sam- "one," from *som-) + âhang "melody, pitch, tune; harmony, concord," from Proto-Iranian *āhang-, from prefix ā- + *hang-, from PIE base *seng^wh- "to sing, make an incantation;" cf. O.H.G. singan; Ger. singen; Goth. siggwan; Swed. sjunga; O.E. singan "to chant, sing, tell in song;" maybe cognate with Gk. omphe "voice; oracle."

A number whose reciprocal is the → arithmetic mean of the reciprocals of a set of numbers. Denoted by H, it may be written in the discrete case for n quantities x₁, ..., x_n, as: 1/H = (1/n) Σ(1/x_i), summing from i = 1 to n. For example, the harmonic mean between 3 and 4 is 24/7 (reciprocal of 3: 1/3, reciprocal of 4: 1/4, arithmetic mean between them 7/24). The harmonic mean applies more accurately to certain situations involving rates. For example, if a car travels a certain distance at a speed speed 60 km/h and then the same distance again at a speed 40 km/h, then its average speed is the harmonic mean of 48 km/h, and its total travel time is the same as if it had traveled the whole distance at that average speed. However, if the car travels for a certain amount of time at a speed v and then the same amount of time at a speed u, then its average speed is the arithmetic mean of v and u, which in the above example is 50 km/h.

→ harmonic; → mean.

A motion that repeats itself in equal intervals of time (also called periodic motion).

→ harmonic; → motion.