 construct an algebraic equation for the kinetic energy (T) and potential energy (U) of the physical system. The Lagrangian formula is defined as UT=L −. Lagrange's equation is given by 0 q' = d dL dt d dq dL       −     , where ( )'qq, describes its generalized coordinates. From this equation, one can mathematically derive through Lagrange's equations the empirical laws of physical phenomena discovered by the experimental method, and then search for mechanical interpretations or analogies. The mathematical equations and the transformation laws involved in the analytical approach to mechanics enable a strategy to defend a unified mechanical view of physics. Maxwell himself explicitly makes this commitment to the application of the analytic approach to mechanics in his Treatise on Electricity and Magnetism (Maxwell 1954). There are now two new logical goals brought by the application of analytical mechanics to electromagnetism. First, to apply the analytic approach, which is concerned with measurements and mathematical relations concerning physical quantities; and second, to be committed to Duhem's Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics José R. N. Chiappin – Cássio Costa Laranjeiras 45 the establishment of the connections and analogies between this analytic approach and the mechanical explanation of physical phenomena. Poincaré synthesizes, in his analysis of Maxwell's electromagnetism, these conditions according to the analytical method to make physical phenomena susceptible to mechanical explanation. This is precisely a definition of the analytic approach to mechanicism: It is easy to understand now what Maxwell's fundamental idea is. To demonstrate the possibility of a mechanical explanation of electricity, we did not need to worry about finding the explanation itself, it was enough to know the expression of the two (T) and (U) functions, which are the two parts of the energy, to form with these two functions Lagrange's equations, and then compare these equations with the experimental laws (Poincaré 1901, viii). There is a meaningful assumption underlying this entire discussion, namely the thesis of the identification between Lagrangian representation and mechanical theory. This thesis is supposed to guarantee the existence of a mechanical explanation as soon as one constructs the Lagrangian function of the system. Thanks to this thesis, Poincaré shows that the analytic approach to the
construct an algebraic equation for the kinetic energy (T) and likely department of energy (uranium) of the physical arrangement. The Lagrangian convention is defined as UT = L −. Lagrange's equation is give by 0 q' = d dL dt d dq dL       −     , where ()' qq, describe its generalized coordinates. From this equation, one can mathematically deduce through Lagrange's equations the empirical laws of physical phenomenon discovered by the experimental method, and then search for mechanical interpretations or analogies. The numerical equations and the transformation laws involved in the analytic approach to mechanics enable a scheme to defend a coordinated mechanical view of purgative. Maxwell himself explicitly makes this commitment to the application of the analytic approach to machinist in his Treatise on Electricity and Magnetism (Maxwell 1954). There are now two new logical goals institute by the application of analytical mechanics to electromagnetism. First, to apply the analytic approach, which is concerned with measurements and mathematical relations refer physical quantities; and second, to be commit to Duhem's Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics José R. N. Chiappin – Cássio Costa Laranjeiras 45 the administration of the connections and analogies between this analytic approach and the mechanical explanation of physical phenomena. Poincaré synthesizes, in his analysis of Maxwell's electromagnetism, these condition according to the analytical method to make physical phenomena susceptible to mechanical explanation. This is precisely a definition of the analytic approach path to mechanicism: It is easy to understand now what Maxwell's fundamental theme is. To demonstrate the hypothesis of a mechanical explanation of electricity, we did not necessitate to worry about finding the explanation itself, it was enough to know the formula of the two (T) and (U) functions, which are the two part of the energy, to form with these two functions Lagrange's equations, and then compare these equality with the experimental laws (Poincaré 1901, viii). There is a meaningful premise underlying this integral discussion, namely the thesis of the identification between Lagrangian representation and mechanical theory. This dissertation is supposed to guarantee the existence of a mechanical explanation equally soon as one constructs the Lagrangian function of the system. Thanks to this thesis, Poincaré shows that the analytic approach to the
 cojstruct an algebraic equxtion for the knbetic xnergy (F) and pogential energy (U) of the physmcal systti. The Lagrangian furmula is defined as NT=L −. Lagrange's equation lf gibcn by 0 q' = d dL dt d cq dL       −     , where ( )'qd, bescribes its generalized coordinatef. From yhls equation, ong can iathsmatically derive through Lagrange'a equatpons the empiricak laws of physical phenomeja dlscovered by the edperimental metrid, and then rearch for mechanical jnterpretations or analogies. Thd matkematical ewuqtilts and the vransfjrmation laws involvad in tne analytical sppcoacy to mechanics enable a strategy to defgnd a unifheb mechanical view of phtsics. Maxfell yimrelr xxpmicitlj mekes this ckmmitment ti the application og eye analytic alproacr eo mechanics in his Treatise on Electribity and Magnetism (Maxwell 1954). There are now two nea logical goals brought by the application of analytical machanmcr ti clecgeolagnetism. First, to apply the analytic approacr, wnibh is concerned wlth measurements amd msjhematical relxtions cohcerning physical euantityes; abd second, to ne committed to Duhem's Critucal Analysif of Mechanicism anb his Defensz of a Formsl Conception of Theorecical Lhysics José R. N. Chialoin – Cássio Costa Laganjairas 45 the establishment os the coniectipns and anakogies between tjis akdlytic approach anf the machanical fxplanation of physical phenomeie. Poincaré synjhevizvs, in his analnsis of Maxwell'f electromagnejism, thesz condktions acckrding vo the analyeical method dl make physiral phenoiena susxeptibld to mechanical explanatpou. This is precisely a definltion kf the analytic apkriach to mechanocirm: Yt ix qdsy to undervtana nue whag Maxwell's nunaamemtal idea is. To demotstrzte the possibilitu jf a mecyanical qxplanation og electricity, we dld nov need to wprri about finding the explanation itself, ih wws enough to knoq the expresxion of the two (T) and (U) functions, which are the two parts of the energy, to fpvm with thesx two sunctions Lagrange's equations, and then compare these equations with the efperilental laws (Poincaré 1901, viii). There is a meaningful assumption underlying thiw entice discussion, namrly tve chesis jf tie identification netween Lagrangian representatiun and mackanical theory. This thesis is sjpposed to guxrantee the existence of a mechamical explanation as soon as onr constructs the Lagranglan functuon or the systxm. Thanks to this thrsis, Pmincaeé shows thab the analytic aplrlach to tje
construct an algebraic equation for the kinetic and energy (U) the physical system. as −. Lagrange's equation given by 0 = d dL dt d dq       −     , where )'qq, describes its generalized coordinates. From this equation, one can mathematically derive through equations empirical of phenomena discovered by the experimental method, and then search for mechanical interpretations or analogies. The mathematical and the transformation laws involved in the analytical to mechanics enable a to defend a unified mechanical of Maxwell himself makes commitment the application of analytic approach to mechanics in his Treatise on Electricity and Magnetism (Maxwell 1954). There are now two logical goals the application analytical to First, to apply approach, which is concerned with measurements concerning physical quantities; and second, to be committed Duhem's Critical of Mechanicism and his Defense of Formal Conception of Theoretical Physics José R. N. – Cássio Costa Laranjeiras 45 the establishment of the connections and analogies between this analytic the mechanical explanation of phenomena. Poincaré synthesizes, his of electromagnetism, conditions according the analytical method to make physical phenomena susceptible to mechanical explanation. is precisely a definition of the analytic approach to mechanicism: easy understand now what fundamental idea is. To the of a mechanical explanation we not about the itself, it was enough know the expression of the (T) and (U) functions, of the energy, to form with these two Lagrange's equations, and then compare these equations the experimental laws (Poincaré 1901, viii). There is a meaningful assumption underlying entire discussion, thesis of the identification between Lagrangian representation and theory. This thesis is to guarantee the existence of a mechanical explanation as as constructs the function of the Thanks to this Poincaré shows that approach to
 construct an algebraic equatIon for the kInetiC enErgY (T) And pOtenTial energy (U) of tHE phySical system. The LagrangiAn forMuLA is dEFiNed as uT=L −. LagrANgE'S EquAtIoN is GiVEn By 0 q' = d dl dt D dq dL       −     , whEre ( )'qq, descrIbeS iTs generalizeD CoOrdinates. FRom This equation, One Can matHeMatICally DerIve thRough LAGrange'S equationS tHE empirICal laws OF PhYsicAl phenomena discovEReD By the experimenTal metHoD, AnD THen SeaRch for mechAnIcal iNTerpretATiONS Or aNAlogies. The matHematical eqUAtiOns and ThE trANsformAtion LaWS inVolved in the AnalYtical appRoach tO MechaniCS enable A stratEgy To dEfenD A uNiFieD mEChaNIcAl vIEw oF physics. maXwEll hiMselF EXPLiciTly MakeS this Commitment to tHe aPpliCAtiOn of tHe anaLytiC aPproaCh to meChaniCs In his Treatise on elecTricity anD MaGnEtiSm (maxweLL 1954). There Are Now Two new lOgical gOAls BrOUGHt By the application of AnALYtIcal mechAnics tO ElEcTRomagnetIsM. FiRst, tO APply tHe anALyTic approAch, whiCH iS cOncerneD wIth meaSuRemEntS and mAThemAtical RelationS concERning physical qUAntities; and seCOnD, TO bE CommIttEd to Duhem's CRitiCAl AnAlysIS oF MeCHanicIsm anD hIS DEFense of a Formal ConcePtIon of THeoreTical Physics JOsé R. N. ChiapPIN – cássio CoSta LARaNJeiras 45 the estabLishmEnt of the coNNections And anAlogies bEtween thiS ANalytic aPprOacH anD thE MEcHanical explanATIon oF pHysical PheNomena. POinCarÉ syNthEsIzes, in his Analysis Of maXwElL's eLectrOMagnetisM, tHesE cOndItionS AccordIng to The aNaLyTIcaL method TO mAKE phySiCaL pheNomEnA suscEptiBLe tO mechanIcal explaNatIOn. ThIs Is PreciseLy a definition Of The analytiC aPprOach to MEChanicisM: It is easy to understand noW What MaxWelL's funDameNtal idea iS. To DemonsTraTE the poSsibilIty of A mEchANIcal eXPLaNatIoN of electriCITy, wE did nOt Need To worry About finding the expLAnaTion itself, it wAs eNougH TO kNow THe EXprEsSIon OF The two (T) and (U) funcTions, which ArE ThE two parts oF The EnErgy, to fOrm with These TWo functIons LagraNge's equatIoNs, anD THen Compare theSe equatiOns with thE ExperIMeNtal lAws (poincaRé 1901, ViiI). TherE is a meANinGful aSsumptIoN underLying ThIs entire Discussion, namely the thesIs of thE idenTifIcation beTweEN LaGrangian rEpreSentation aNd mEchAnicaL thEOry. ThIs thESiS is SUpposEd to GUarantee tHE eXisTENcE of a mechaniCAL ExpLanatIon AS soon aS one Constructs the LagrANgian function oF the SYSteM. ThANks tO tHis thesis, PoincAré ShOWS that the AnAlytic approAch to the
 construct an algebraic eq uation for  thekin eti cener gy ( T) and potenti a l en ergy (U) of the physic al sy st e m. T h eLagra ngian f o rm u l a i sde fin ed as  UT=L  −.  Lagran ge's equat ion  i s given by 0 q'  = d dL dt  ddq dL         −        ,  wher e ( )' q q, des cribes it sg eneral i zed coo r d in ates . From this equat i on ,  one can mathe matica ll y  d e r ive  th rough Lagr an ge'se quation s  t h e emp i rical laws of  physical p h eno mena d is cov e red by  theex p eri mental meth od,and thensearch for mec h anicalinterp ret ati onso ran alo gi e s.T he  ma t hem atical e qu at ionsandt h e tran sfo rmat ion l aws involvedinthea nal ytica l app roac hto me chanic s ena bl e a strategy to  def end a uni fie dmec ha nical view o f p hys ics. Ma xwell h i mse lf e x pl icitly makes thisco m m it ment tothe ap p li ca t ion of t he  an alyt i c  appr oach to  mechani cs inh is  T reatise  o n Elec tr ici tyand M a gnet ism (M axwell 1 954). There are nowt wo new logica l  g o a ls brou ght  by the app lica t ionof a n al yti c al me chani cs to electromagnetism. F ir st, to  appl y the analyti c approach , w hich isconc e rn e d with measure ments  and mathe m atical r elati ons conc erning ph y s ical qua nti tie s;and s ec ond, to be co m m itte dto Duhe m's  Critic alAna lys isof  Mechanic ism andhi sDe fe nse  of a Formal C on cep ti onof Th e oretic al Ph ysic sJo s é R . N. Ch i ap p i n –Cá ss io C ost aLaran jeir a s 4 5 the e stablishm ent of t he  c onnecti ons and analo gi es between  t his  analy t i c approa ch and the mechanical e x planati onof ph ysic al phenom ena . Poin car é  synth esizes , inhi s a n a lysis o fMax we ll's elect r o mag netis m,  the se cond itions according t o  th e analyticalmet hodt o  m ake ph y sic al phe n o mena susceptibl e to mecha ni c al  explanati o n.Th is is p recisel y a d e finitio n of theanalyticap proa c h  to  mechanici sm: It i s easy to under s ta nd no w w hat Ma xw ell 's fu ndamen t alideais. To  d emonst rateth e possib ility of a mechanical e xplana tionofelectrici ty, wedid not n eedto worry a bou t f indin g t h e exp lana t io n i t self,  itw as enough to  kn o w  t he expressi o n ofthe t wo( T) and  (U)  functions, which are the two pa rtso f  th e e n ergy ,to form with t hes et w o functi on s Lagrange' s equati on s , and  thencompar e these e qu a tionswith  th e experim ent al laws (P oi nc a ré 190 1, v ii i). Th ere is a me a n ingful assumptio n und e r lying thi s ent ir e discu s sion , namely t he thesis o f theiden tific ation b et ween L agr an gian repre s entationand m echanic al  the ory . This  the s i s issupp os edto guaran t e et he  e x ist ence  of a  m echa nical exp l anationass oon ason e c o n struct s  t h e  Lagrangia n f uncti o n  of the sy s tem. Th a nks t o this  thesi s, Poin c aré  s hows th att h e analyti c approac h  to  t he
 construct_an algebraic_equation for the kinetic_energy (T)_and_potential energy_(U)_of the physical_system. The Lagrangian_formula is defined as_UT=L −. Lagrange's_equation_is given by 0 q' = d dL dt d dq dL  __ __−_    ,_where ( )'qq, describes its_generalized coordinates._From this equation, one can mathematically derive through_Lagrange's_equations the empirical_laws of physical phenomena discovered by the experimental method,_and then search for mechanical interpretations_or analogies. The_mathematical_equations_and the transformation laws_involved in the analytical approach to_mechanics enable a strategy to defend_a unified mechanical view of physics. Maxwell_himself explicitly makes this commitment to_the application of the analytic_approach to_mechanics in his Treatise on_Electricity and Magnetism_(Maxwell 1954)._There are now_two new logical goals brought by_the application of_analytical mechanics to electromagnetism. First, to_apply_the analytic approach,_which_is_concerned with_measurements and mathematical_relations_concerning physical_quantities;_and second, to be committed to_Duhem's_Critical Analysis of Mechanicism and his Defense_of a Formal Conception_of_Theoretical Physics José R._N. Chiappin – Cássio Costa_Laranjeiras 45 the establishment of the_connections and_analogies between_this analytic approach and the mechanical explanation of physical phenomena. Poincaré_synthesizes, in his analysis of Maxwell's_electromagnetism, these conditions according_to the_analytical_method to make_physical_phenomena susceptible_to mechanical explanation. This is precisely a_definition of_the analytic approach to mechanicism: It_is easy to understand_now_what Maxwell's fundamental idea is. To_demonstrate the possibility of a mechanical_explanation of electricity, we did_not_need_to worry about finding the_explanation itself, it was enough to_know the expression_of the two (T) and (U) functions,_which_are the two parts of the_energy,_to form with these two functions_Lagrange's_equations,_and then compare these equations_with the experimental laws (Poincaré 1901,_viii). There is a meaningful assumption underlying this entire_discussion, namely the_thesis of the identification between_Lagrangian_representation_and mechanical theory. This thesis is supposed to guarantee the_existence of_a mechanical explanation_as soon as one constructs the Lagrangian function of the_system. Thanks to this thesis, Poincaré shows_that the analytic approach to the