Beispiel 3.4 (Schwerpunkt eines homogenen Starrk\303\266rpers)Erstellt: 19.2.2020
Ersteller: W. Kemmetm\303\274ller
\303\204nderungen:restart;
with(LinearAlgebra):
with(VectorCalculus,Jacobian):
with(VectorCalculus,SpaceCurve):
with(plots):MFNWtKUb<ob<R=MDLCdNVZMK;hX>D:;B_ccLI]ZRLCTJcDXoHuux;ktNiij;VV?h;mHbkGNsBd;C\\?igWuPiITQgomTnOWuUIheiOUWAgXNqtHygomtketd?CrSYeABAeM;do=tp<XMJEuMmxxqk^xPqdV>hl>`kqyxjAyV`mV`j^ymZtOa]vBPSDMSnKZhJnEM<JgDnIA\\N_u=`jnaxV`i@Ibm^pg?gkowK_iFOepawxh]Rf;cvA;vyMvLYhUSUTosUYYhAwGAW@URm[YskfUQs]uTPuiKyb[?BJuGRQuE;gbwWHoUkEUpwwd]XLSR[GSxOxyOdY=UFAQJuURuvA<obmxglQrESR@wyYv[uRUUP@\\R]]LPTlw_tantsIZdXmwOjFaq<XekFoFH;;fvABGssx>linppQZdWlwWftfpf_gcOsbFoQxncHmy_usOeN_savn<>nvEOqsxCr\\GVhiYWOej;Td]vIWuImUWAyACuAPwZUWi<nXDuAdPGqqV`y<mj<<J_yZSybpI:Ey;[VYEGaoRP_CHCuA\\vEhyvAJO]sxHWwdmFaknywa\\nm\\R^u]JX^PIy;ZuvfG^\\C`bFF\\Sy:cvA;WxmxcIwlYhcGISyfiwreGC:Ox=[hRQSlwSeMhiWTmUe_Wfv;EY\\T>TysIJoAlwuUNUNuqvGlXWtwKQStEJQqVp\\kXPu_uucyk@uwITY>AL;<nvAJlxoLawM\\XbMVg\\YkLVdqmwmX`qNFD\\dXjGPc:P_`w]BqA;GypJ`uuNqMgEsxLpI>dx?jP_fYxtUWjBqalx[:>_y>jfYZSy:>bpIjfY:Ox=;sx;dw=:>^uENwE:KhI[VYLu;xSlmJ^yweuyeTSHDlw]VY>ds^y@NZBqaJLNxM:LpI\\VY^lY>ZlxkfY^uENFuQotNNpI`w=ZJQlfYu?oxKhI;Tx=jI\\F[dFwSoEBN]HuQRhyrXIcGedXWHPiukGh_GG]mSpI:;WNmxC[YhkIRaDnuRtmcEUDeMsI_w=dX;qXb<ROT@>NDuALpI>DvZlx;KK:mHNfVFv;^t:ydxGfEw[Yo^uAsxBNaDy?g:KhI_w]SQZ`y:<lw]VY>NvKA[:PXcGDqiCiuUAdw]VYJg@sxtwSYjCqQlx[bx\\Hhw?^dnVyxP]Uiw]InhQtmOmTGhdq`lx;>b]QpI?^N?[[NbpIZ:`ikhoD>d?aw=FULc:SZbl<<>bO?uIy[rymOni[WsBqalx;cs?yWlDuAWZ::K@\\\\:`WZZHaSy`cX]Sybp=KuKgYxSXBqIlwC:jAJb:::;<:;\\:JBqA<TU\\mqxL^umDpVYIrexkIyQDxlXXxhAjHpkpmvv`l^u]ZlftUXDqv`yB=mTdVY@v>imaXm<pwBusSTtchN_yRpIJ:eUjHYE\\VYtQ?\\VYZl<>jtxfYY]^w]SyZ:JJQlfYx_TyBqA^F>::B:::BJ::;fj[ewgCT?VSIvEYGvaHgSypkSeyFvEdw]^Zvbf@[;FuANP:::\\tymxG]wTQmfYNuCDyCTEdwUiaqC[SyBqQ:LsI\\fJhI;<B::ZS=>jf=>BBZoEkmuX=gtgfAoGwevyebfYFu<JdqkYQmZTy:mh:NS;;<jl;<Bcr`uu>KhIBNIBA=Y:eelwWIoH_uuPAvjYDqmeDussQWfuhHcSfGsx;B:>SUt>gRacEBSY^cIamuZuTlwC:;TQ[WoSBSyBl<::tAJN:JZFlw_fYBoic]UYKueP_Et_xoCuAm`Jo\\xWp<`w=FULC@B:>jtNfyvaJhidNsHasrhlWHqna]]WZOfy;h^uEZNgPhiuxvJhiyWxOAqhQrQPwynclx;cH<yGT=gDmxcYwkqWNuI^u=RpIdwJSyRpI<Bl<sx>ZDy[^w]BE:;FY[EUYC?Ky\\Av?idAugLgY^uE:;R?=xewD^uEBZBqaJD:;<Z:dnoWysiv_iv?eR?e>ar>EV<QsDQgSUh`mHpkHvwCBqIJ>:IWH_gf_ggSUp_Ex[Yr[Hn[HysIYMydoxgYuyoxTYWmqvGYWVAiksWBcB_uurucP]VYC]:PxMoZ[HyxVyfYp^av^GfTAr:AftaxcYj@f[l^`n^qqwwXqoWWqhquwXyWyhYioXgqtWv@ikmvfHavwFnB`wUY`qiflxKAJbtQ?QOhlOxuvWxXppWWQOx@wbAwbywiyw\\Qv\\DUZEsLhNiiqqqmj@RhmWhaoSUplQxlaj_IYU=lw=^;>j@OtjyuAymyoys`^ua[Gf[Ip]wN_WhitfnetGYeqsxditE]YkyUyQyQiwUyhsUUJgYZblYTmCf[GfYyYyii^QfawfaWhmWX?SRZWgu?YkQVkaXhmWhyTYeY?Yu<_w]SyB>JHm_TSP@SY]MulXfeVEmKV<QJuSIuSvdyuywyxn`pnDiy;aR?mRPlLPLlw=Nu?ZdIl@qway\\MV\\M>\\J>^wvnwWypilg^g`of`Iv[IhcQt_FftvayvyIyaya]kNf>`iYvsqwuvWab?sZy``fc\\VyJguyfeHfelIqjwetosxxpYGw`AuJ`w=>ZNQm@qyhoasOx^GmsnhpohlnliGt\\hj^OehYqtib>xjY`y]ykGVwPy\\N^\\Jhibpn^`sVyrCG]LyeshZDheg_cpIZ:prMAuooiIn]v>_mvfeqtgP^K@olhv]Xn]h^MQvIyiKXnoXoQA[yqawOynyaAniU``_Op@^[iQvYy_xWhF`wMA_^C:[LolTxpuxdynYTSyPKitwEtelLPlLhpohPXv]NKDv[yYV@Q[lmXAxEQyQqbWAtJAlfYZSE:;GyCikSHmSGmsfZ?f:]upMSpoWGQUCaxmwfIqYUyYZMsnGg^uEBqQ:dvMAuYYtGQmoTOmtNuTQUmOqaUV]UVmY`ETKET?XKA]jAxmrlYVMYHqnGXMDamxlkfYJSyZZ`]TVqHyoYwqxgf`abAwbQHyRvvTFsBAsR?pZGr[YrAhjhWmsVh`y[y^yZxoyytbisUx@muvGyAyEy]UxqTLYGvarNyXoweF_w]aev_VYfpZHpyhow^avNep`gcfaaasSX`OoudfawfiYqqwG[CF[_yvqqwWYiEqlgFxkIxcHocXoPgoTn`f?mrYfyqqyqyuwiywyInarAnviqOxe[y^pHvQxeNqgoxmfawm>tQYvaGkfY:KgIUdIYuu_VCQdsSX`AShketcXdOrxSdp?WKQfyuyuyuy[yjYRSgDrMr?ar>XKP\\ObAukXVV]UVipeuthuuxhuphWUUR=UR[HvHymytW\\MT;yoCixeutO=yWMV]MVpywUyPgMynMpI\\F;RsIsAagSUhpwWYqETKEdkir]vBIdUsHh]XdatcOh_YB=SB?_wMKVhihQqUMoeYMTLMX\\arCWsQwGu;Ir;SIyijEv<AikUvviywYuoWWQmyXqw@]RVsIp]glwwoGXwyGMkFH]HlKH\\Sy:m`JO]GouqVcQwdqAx[YrLXdq_\\Qv\\ypytYwKHlKh\\h^yuywyXkIwwppfGQmphgUQcYg^LFkXvax_e`VyHx]yna`_sRFnfVioQwOGvWnlYYrIOeV_eVqywWyBqaJL:PPciOYmqVUjYpmCHkCapcUthquwXMKDL[\\UFeSGeukXVAMUTMmohpoHpkHpJ`XItMx\\QkMv>aqsUxxxyxYyvayvySxDy^PrIhyeTxK<tXmUXuMw]xKIl]tRtyxiyU[yxOlqYQkdpJpLNv\\YTYmiMSHTL[TyJmr]`raiJ?erghwf\\NYuopEWOAs\\pS_mRpitEXsKHkxyP]hnaaklUWKiukHL]TJ:EyniPxIMDDlqYyiyquIysiYqiuqEn[HncIwcyuQPOm@UQpOWmqwqxUIV=qjOEYAPrwAytQyDtXOmVg<nnDue\\y>qUfpxUYqqMyFHM^uMd\\x[ALqDvEmkq=SpIJ:\\xo`vsmkhdLSDMS<MR<YcQt_`j>`j^av^ULMTLuUYuuVauV[<y^]wyyNK=UR=yXYYiiQx]yR=sxTXmUxDqLuXMKDT[INwhvg]y_Ur>ISM`TjuWyxsyuqriOSynS=sx<ZgN_yF`AwbAIm_PgkWuaysYxcR@`[Hf=qjAwkXf`j>`JHp^QyoXwDOcDOomwmkIxkYiqwwSH`MYlfYZSy:DJYpqUeOIumxdwMynIXmUX]iwwlFuaywiyasOx^Gs?GuA`xPxpcWr@`uVaelx[^C:;T<cY@?fDEGcCG=ubHcemsVHaysYxEaUoawSYhqyuyuYSQh_MdscSUoHwcEN;U`Eh>?irGsi]SleXmUUuYstQxqyU`AxKKhI[>OxewEsCIsSf@ecDocHouoWWQibEsDVqyeSIuSy>IcMsIvAx=Wf]WfawvyqHQQeU=UBsU_uRSuw?UHSCESchbEt<eVYGGSyRpIJJ_pWalcVdDPkDpkYvaXapcWtiyqyqiCQl_NtQqphguTytQydQwdgy`TxdPhiixh[VyBqa:jMqKuyxiyYvAyk=Xj=p?Ewd]qGYmqtXdatcmuvHY<UKDtLApKWLwgiwWAp[URGlsxhQmEsxL`:>Jah=uthgU=UR=esFas^SXXyYyiyCUd`cUyoYwgXeqtgOUoOt:wvBmxKgY:;BDyCi;CsuTxmfWgm[TR@@W@YL^TyBqQ:<jPEvMeUnxLSyRpIZJCBqIlDe:>bsIjfYZSE:>bpIJ<JNokjAthvmwyv<yhAyoKhiT`vVYrrHhUnc^q\\NFlw?Z:P_kpsI`w]BoqsxGvemcLgY:dt>QQyLpI`wMuT[xK\\qRfhQTHlU=RpIJ:<?LwgiUY@vGERq]naaJy]QpxoMULlxK:<Te]WgitdawUiSpIoaLpI>JAT]awm[FuAsx;B:oH[UWiCMdmlwUrQOmSxbpMNxMBqQGpXmIUDQnYqOJhIcvAfsq@fyIyVPhY>vLU^ERpIB:KgCgyvAsx;gGOCmwGjErRMhI;B:XNuAsxdKalsxpVPiKRL[:Pg\\Wgipbsaxyv\\xx^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3.4Masse der Teilk\303\266rper V1 und V2eq_m1:=m1=rho*l/3*l*3*l/4;
eq_m2:=m2=rho*l*l*l/4;Schwerpunkt des ersten Teilk\303\266rpers V1rS1x:=eval(rho/m1*int(int(int(x,x=0..l/3),y=0..l),z=l/4..l),eq_m1);
rS1y:=eval(rho/m1*int(int(int(y,x=0..l/3),y=0..l),z=l/4..l),eq_m1);
rS1z:=eval(rho/m1*int(int(int(z,x=0..l/3),y=0..l),z=l/4..l),eq_m1);Alternative FormulierungrrS1:=eval(rho/m1*map(int,map(int,map(int,<x,y,z>,x=0..l/3),y=0..l),z=l/4..l),eq_m1);Schwerpunkt des zweiten Teilk\303\266rpers V2rS2x:=eval(rho/m2*int(int(int(x,x=0..l),y=0..l),z=0..l/4),eq_m2);
rS2y:=eval(rho/m2*int(int(int(y,x=0..l),y=0..l),z=0..l/4),eq_m2);
rS2z:=eval(rho/m2*int(int(int(z,x=0..l),y=0..l),z=0..l/4),eq_m2);Alternative FormulierungrrS2:=eval(rho/m2*map(int,map(int,map(int,<x,y,z>,x=0..l),y=0..l),z=0..l/4),eq_m2);GesamtschwerpunktrSx:=eval(1/(m1+m2)*(m1*rS1x+m2*rS2x),{eq_m1,eq_m2});
rSy:=eval(1/(m1+m2)*(m1*rS1y+m2*rS2y),{eq_m1,eq_m2});
rSz:=eval(1/(m1+m2)*(m1*rS1z+m2*rS2z),{eq_m1,eq_m2});Alternative FormulierungrrS:=eval(1/(m1+m2)*(m1*rrS1+m2*rrS2),{eq_m1,eq_m2});