 while working at the Harvard College Observatory in 1936.

Early life
Muriel was born on 3 February 1909 in Danvers, Massachusetts, the daughter of George and Stella Mussells.

Scientific contributions
Mussells Seyfert was employed as a human computer at the Harvard College Observatory.  She is best known for discovery of new ring nebulae in the Milky Way.

Personal life
In May 20, 1935, Muriel married Carl Keenan Seyfert after whom the Seyfert galaxies and the Seyfert's Sextet were named.  The couple had two children. 

Sylvia Mussells Lindsay, wife of Eric Mervyn Lindsay, was Muriel's sister.

References

Category:1909 births
Category:1997 deaths
Category:American women astronomers
Category:Harvard Computers
Category:20th-century women scientists
Category:20th-century American scientists Virtual displacement

In analytical mechanics, a branch of applied mathematics and physics, a virtual displacement δri "is an assumed infinitesimal change of system coordinates occurring while time is held constant. It is called virtual rather than real since no actual displacement can take place without the passage of time." Also, virtual displacements are spatial displacements exclusively - time is fixed while they occur. When computing virtual differentials of quantities that are functions of space and time coordinates, no dependence on time is considered (formally equivalent to saying δt = 0).

In modern terminology virtual displacement is a tangent vector to the manifold representing the constraints at a fixed time. Unlike regular displacement which arises from differentiating with respect to time parameter t along the path of the motion (thus pointing in the direction of the motion), virtual displacement arises from differentiating with respect to the parameter ε enumerating paths of the motion varied in a manner consistent with the constraints (thus pointing at a fixed time in the direction tangent to the constraining manifold). The symbol δ is traditionally used to denote the corresponding derivative

Comparison between virtual and actual displacements

Here we consider the total differential of any set of system position vectors, ri, that are functions of other variables 

and time t.  These position vectors are "on-shell" meaning they satisfy the Euler-Lagrange equations and solve for the true evolution trajectories of the system.
In other words, these vectors move according to the constraint forces and actual forces of the system at every instant in time.  The actual displacement is the differential of the
while working at the Harvard College Observatory in 1936. 

 Early life 
 Muriel was born on 3 February 1909 in Danvers, Massachusetts, the daughter of George and Stella Mussells. 

 Scientific contributions 
 Mussells Seyfert was use as a human calculator at the Harvard College Observatory.   She is best known for discovery of newfangled closed chain nebulae in the Milky Way. 

 Personal life 
 In May 20, 1935, Muriel marry Carl Keenan Seyfert after whom the Seyfert galax and the Seyfert's Sextet were named.   The couple had two children. 

 Sylvia Mussells Lindsay, wife of Eric Mervyn Lindsay, was Muriel's sister. 

 References 

 Category:1909 parentage 
 Category:1997 deaths 
 Category: American woman astronomer 
 Category: Harvard Computers 
 Category:20th - hundred women scientist 
 Category:20th - hundred American scientists Virtual displacement 

 In analytical mechanics, a arm of applied mathematics and physics, a virtual displacement δri " is an assumed infinitesimal change of arrangement coordinates occurring while time is held constant. It is predict virtual rather than real since no actual displacement can take place without the enactment of time. " Also, virtual displacements are spatial displacements exclusively - time is fixed while they occur. When computing virtual differentials of measure that are functions of space and prison term coordinate, no addiction on time is considered (formally equivalent to saying δt = 0). 

 In modern terminology virtual displacement is a tangent vector to the manifold representing the constraints at a fixed meter. Unlike regular displacement which arises from differentiating with respect to time argument t along the path of the motion (thus pointing in the direction of the motion), virtual displacement rise from differentiating with respect to the parameter ε enumerating paths of the apparent motion varied in a manner consistent with the constraints (therefore pointing at a fasten time in the direction tangent to the constraining manifold). The symbol δ is traditionally use to denote the equate derivative 

 Comparison between virtual and actual displacements 

 Here we consider the entire differential of any stage set of system side vectors, ri, that are function of other variables 

 and prison term t.   These position vector are " on - shell " meaning they satisfy the Euler - Lagrange equations and solve for the true evolution trajectories of the system. 
 In early words, these vectors affect according to the constraint forces and actual forces of the system at every instant in time.   The actual translation is the differential of the
 whlle working at the Harvavd College Obserrqtory mn 1936.

Earlg life
Mufiel was born on 3 February 1909 mn Dqnverw, Massachusetts, the dajghter of George qnd Wrella Mussxmls.

Sciekcific gontrnbntions
Mussells Xeyfert wav employed as d fulan computer at the Harvard College Observstlry.  She is beft kmjwn ror discovery of new ring nebulae jn the Kilky Way.

Perspnal life
In May 20, 1935, Muriel mwrrifd Carl Keenan Seyvert after qhom rhe Seyfert ealaxies and the Seyfett's Sextet were named.  The coupld had two childtzb. 

Sjnvia Musselos Ligdsay, wife on Eric Kervyn Kindsay, was Muviel's siwter.

References

Categorb:1909 births
Category:1997 deajhs
Categorf:Ajerican women asteobomerv
Catagorh:Yarxars Romluters
Fatxgory:20th-centhry women sxientists
Category:20th-vegniry American scieneifts Virtual displacement

In analytical mtchanjcs, a branch of applied mathematics and physlcs, a vireual displacement δri "is an assumed infinitesimal whangx uf wyfgwm coordinates occurring while time is held conffamt. It is called yirtual rather tham gesj since no acjual displzcement can take ppace wijhout rhe passade og time." Also, virtual displacwments are siatiql displacements erclusively - cime ix fixrd while they occur. Wheu comphting virtuwl differsvtials of quantigiex dhat are functions of spacq and timx cooxdinates, no cependqnce on tile is considered (formallj equnvalett to sayijg δt = 0).

In modern terminology virvnal displacemgnt is a tangeut vecbor to the manisold representnng the eonstrxints at a fixed vime. Unlike wegular displdfement which arises srom difderentixging with resprct to time parametwr t along the patm of jhs motion (thus piinuibg in the direvtiun jf tie moehon), virtual gispuacdkent xrises from aiffrrentiating with res[ect to the parameter ε ekumeratint paths jf the motion varied in a manneg convisvent woth the constraints (thus pointing at a fixfd bime in the dyrecbion tangent tp the constraining manifold). The symbol δ is traditionally ysed to denote the eovresponding verivaeive

Compasison between virtuao and actual dispkacements

Here we consjder tve tohal differential of any set of system position vectors, ri, that are functiins of other variagles 

and nimz t.  Thesq podmtion vectors are "on-shell" meaning they satisfy tie Euler-Lacrcnge equations and solve for yhd true evolutkon trajectories of the aystem.
In other words, these vectors move according to the constrsint forxes ahd actlzl forces of the sysyem at evert instabt ik time.  The acguak fisplacemfnt ms che differential of the
while working at the Harvard College Observatory Early Muriel was on 3 February daughter George and Stella Scientific contributions Mussells was employed as a human computer the Harvard College Observatory. She is best known for discovery of new ring in the Milky Way. Personal life In May 20, 1935, Muriel married Carl Seyfert whom Seyfert and the Seyfert's Sextet were named. The couple had two children. Sylvia Mussells Lindsay, wife of Mervyn Lindsay, was Muriel's sister. References Category:1909 births deaths Category:American women astronomers Computers Category:20th-century women scientists Category:20th-century scientists displacement In mechanics, branch applied mathematics and a virtual displacement δri "is an assumed infinitesimal change of system coordinates occurring while time is held It is rather than since actual can take place passage of time." Also, virtual displacements exclusively - time is fixed while they occur. computing virtual of quantities that are functions of and time coordinates, no dependence on time is (formally equivalent to saying δt = 0). In modern terminology virtual displacement is a tangent the manifold representing the at a fixed Unlike displacement arises differentiating with to time parameter t along the path of the motion (thus in the direction of the motion), virtual displacement arises from respect the parameter ε paths of the motion in manner consistent with the pointing a the tangent the constraining manifold). The δ is traditionally used to the corresponding derivative Comparison Here we consider the total differential of any of system position vectors, ri, that are of other variables and time t. These position vectors are "on-shell" meaning satisfy the and solve for the true evolution trajectories of system. In other words, vectors move according to the constraint forces and actual of system at instant in time. actual displacement is differential of the
 while working at the Harvard COllege ObseRvatoRy iN 1936.

EaRlY lifE
MurIel was born on 3 FeBRuarY 1909 in Danvers, MassachusettS, the dAuGHter OF GEorge And StelLA MUSSelLs.

scIenTiFIc ContrIbuTions
MuSsells SeyfErt WaS employed as a HUmAn computer At tHe Harvard ColLegE ObserVaTorY.  she is BesT knowN for diSCovery Of new ring NeBUlae in THe Milky wAY.

PErsoNal life
In May 20, 1935, MurieL MaRRied Carl Keenan seyferT aFTeR WHom The seyfert galAxIes anD The SeyfERt'S sEXteT Were named.  The cOuple had two CHilDren. 

SyLvIa MUSsells lindsAy, WIfe Of Eric MervyN LinDsay, was MuRiel's sISter.

RefERences

CAtegorY:1909 biRthS
CatEGoRy:1997 DeaThS
catEGoRy:AMEriCan women AsTrOnomeRs
CaTEGORy:HaRvaRd CoMputeRs
Category:20th-cEntUry wOMen ScienTists
cateGoRy:20th-cEntury ameriCaN scientists VirtUal dIsplacemeNt

IN aNalYtIcal mEChanicS, a bRanCh of appLied matHEmaTiCS ANd Physics, a virtual disPlACEmEnt δri "is An assuMEd InFInitesimAl ChaNge oF SYstem CoorDInAtes occuRring wHIlE tIme is heLd ConstaNt. it iS caLled vIRtuaL ratheR than reaL sincE No actual displaCEment can take pLAcE WItHOut tHe pAssage of timE." AlsO, VirtUal dISpLacEMents Are spAtIAl DIsplacements exclusiVeLy - time Is fixEd while they ocCur. When comPUTIng virtuAl diFFeREntials of quantIties That are funCTions of sPace aNd time coOrdinates, NO DependenCe oN tiMe iS coNSIdEred (formally eQUIvalEnT to sayiNg δT = 0).

In modeRn tErmInoLogY vIrtual disPlacemenT iS a TaNgEnt VectoR To the manIfOld RePreSentiNG the coNstraInts At A fIXed Time. UnlIKe REGulaR dIsPlacEmeNt Which ArisES frOm diffeRentiatinG wiTH resPeCt To time pArameter t alonG tHe path of thE mOtiOn (thus POInting in The direction of the motion), VIrtual dIspLacemEnt aRises from DifFerentIatINg with RespecT to thE pAraMETer ε eNUMeRatInG paths of thE MOtiOn varIeD in a Manner cOnsistent with the coNStrAints (thus poinTinG at a FIXeD tiME iN The DiREctION tangent to the coNstraining MaNIfOld). The symbOL δ iS tRaditioNally usEd to dENote the CorresponDing derivAtIve

COMParIson betweeN virtual And actual DIsplaCEmEnts

HEre We consIdEr tHe totAl diffERenTial oF any seT oF systeM posiTiOn vectorS, ri, that are functions of otHer varIableS 

anD time t.  TheSe pOSitIon vectorS are "On-shell" meaNinG thEy satIsfY The EuLer-LAGrAngE EquatIons ANd solve foR ThE trUE EvOlution trajECTOriEs of tHe sYStem.
In OtheR words, these vectorS Move according tO the CONstRaiNT forCeS and actual forcEs oF tHE System at EvEry instant iN time.  The AcTUal diSplaceMent is The diffEREnTIal of tHe
 while working at the Harv ard Colleg e Obs erv ato ry  in1936 .

Early lifeM urie l was born on 3 Februa ry 19 09 in D a nv ers,Massach u se t t s,th edau gh t er  of G eor ge andStella Mus sel ls .

Scientifi c  c ontributio nsMussells Sey fer t wasem plo y ed as  ahuman  compu t er atthe Harva rd Colleg e  Observ a t or y. She is best known fo r  discovery ofnew ri ng ne b u lae  in  the Milky  W ay.
P ersonal li f e InM ay 20, 1935,Muriel marr i edCarl K ee nan Seyfer t aft er who m the Seyfe rt g alaxies a nd the Seyfert ' s Sexte t were  na med .  T h eco upl eh adt wo  ch i ldr en. 

Sy lv ia  Muss ells L i n dsay , w ifeof Er ic Mervyn Lin dsa y, w a s M uriel 's si ster .
Refe rences 

Cat eg ory:1909 births 
Cat egory:199 7 d ea ths 
C atego r y:Amer ica n w omen as tronome r s
C at e g o ry :Harvard Computers 
C a t eg ory:20th -centu r ywo m en scien ti sts 
Cat e g ory:2 0th- c en tury Ame ricans ci en tists V ir tual d is pla cem ent
I n an alytic al mecha nics, a branch of ap p lied mathemat i cs a nd phys ics , a virtual  dis p lace ment δr i " i s anassum ed in f initesimal change o fsystem  coor dinates occur ring while t i me is he ld c o ns t ant. It is cal led v irtual rat h er thanrealsince no  actual d i s placemen t c antak e p l a ce  without thep a ssag eof time ."Also, v irt ual  di spl ac ements ar e spatia ldi sp la cem entse xclusive ly  -ti meis fi x ed whi le th ey o cc ur .  Wh en comp u ti n g  vir tu al  dif fer en tials  ofq uan titiesthat arefun c tion sof  spaceand time coor di nates, node pen denceo n  time is  considered (formally e q uivalen t t o say ingδt = 0).
In  moder n t e rminol ogy vi rtual  d isp l a cemen t is  ata ngent vect o r  to  thema nifo ld repr esenting the const r ain ts at a fixed  ti me.U n li ker eg u lar  d i spl a c ement which ari ses from d if f er entiatingw ith  r espectto time  para m eter talong the  path ofth e mo t i on(thus poin ting inthe direc t ion o f  t he mo tio n), vi rt ual  disp laceme n t a rises  fromdi fferen tiati ng  with re spect to the parameterε enum erati ngpaths ofthe mot ion varie d in  a mannercon sis tentwit h  thecons t ra int s  (thu s po i nting ata  f ixe d ti me in the d i r e cti on ta nge n t to t he c onstraining manif o ld). The symbo l δi s  tr adi t iona ll y used to deno teth e correspo nd ing derivat ive

Com pa r isonbetwee n virt ual and a ct u al dis plac eme nts

Here  we  c o nsiderth et otal d iffe re ntialof any seto f  system position  vect o r s, ri ,  th at ar efunctio n s of  other var iables 

an d time  t. Thes e posit io n vect ors  a re "on-she l l" meanin g the y satis fy  the  Eu ler-La gran g e  equa tion sand  solve fo r th e  t ru e  ev olut ion t ra ject ories oft he syste m.I n other  w ord s ,  these ve c t ors move a cco rding t o the cons t rain t  f o rcesand ac tual f orces o f  th esystemate v ery insta nt in tim e . Th e ac tual dis pl acem en t i sthe differentia l of the 
 while_working at_the Harvard College Observatory_in 1936.

Early_life
Muriel_was born_on_3 February 1909_in Danvers, Massachusetts,_the daughter of George_and Stella Mussells.

Scientific_contributions
Mussells_Seyfert was employed as a human computer at the Harvard College Observatory.  She_is_best known_for_discovery_of new ring nebulae in_the Milky Way.

Personal life
In May_20, 1935,_Muriel married Carl Keenan Seyfert after whom the_Seyfert_galaxies and the_Seyfert's Sextet were named.  The couple had two_children. 

Sylvia Mussells Lindsay, wife of_Eric Mervyn Lindsay,_was_Muriel's_sister.

References

Category:1909 births
Category:1997 deaths
Category:American women_astronomers
Category:Harvard Computers
Category:20th-century women scientists
Category:20th-century American scientists_Virtual displacement

In analytical mechanics, a branch_of applied mathematics and physics, a virtual_displacement δri "is an assumed infinitesimal_change of system coordinates occurring_while time_is held constant. It is_called virtual rather_than real_since no actual_displacement can take place without the_passage of time."_Also, virtual displacements are spatial displacements_exclusively_- time is_fixed_while_they occur._When computing virtual_differentials_of quantities_that_are functions of space and time_coordinates,_no dependence on time is considered (formally_equivalent to saying δt_=_0).

In modern terminology virtual_displacement is a tangent vector_to the manifold representing the constraints_at a_fixed time._Unlike regular displacement which arises from differentiating with respect to time_parameter t along the path of_the motion (thus pointing_in the_direction_of the motion),_virtual_displacement arises_from differentiating with respect to the parameter_ε enumerating_paths of the motion varied in_a manner consistent with_the_constraints (thus pointing at a fixed_time in the direction tangent to_the constraining manifold). The symbol_δ_is_traditionally used to denote the_corresponding derivative

Comparison between virtual and actual_displacements

Here we consider_the total differential of any set of_system_position vectors, ri, that are functions_of_other variables 

and time t. _These_position_vectors are "on-shell" meaning they_satisfy the Euler-Lagrange equations and solve_for the true evolution trajectories of the system.
In other_words, these vectors_move according to the constraint_forces_and_actual forces of the system at every instant in time._ The_actual displacement is_the differential of the