SOLUTIONS MANUAL... Orbital Mechanics for Engineering Students - Howard D. Curtis - pp.190.pdf

文档介绍：-RiddleAeronauticalUniversityDaytonaBeach,(a)ˆˆˆˆˆˆAA⋅=++()AAAxyzijk⋅()AAAxyzi++jkˆˆˆˆˆˆˆˆˆˆˆˆ=Axi⋅()AAAAxyzijk+++AAAAyxyzjijk⋅()+++Azkki⋅()AAAxyz++jk=AAA2()iiˆˆ⋅+ijˆˆ⋅+AAA()ikˆˆ⋅+AAˆˆji⋅+A2ˆˆjj⋅+AAˆˆjk⋅xxy()xzyx()y()yz()+AA()kiˆˆ⋅+AAkjˆˆ⋅+A2()kkˆˆˆ⋅zxzy()z=AAAAAAA2()100+()+()+()01+AAAAAAAA2()+()0+()0+()0+2()1xxyxzyxxyyzzxzyz=++AAA222xyzBut,accordingtothePythagoreanTheorem,A222++=AAA2,whereA=A,⋅=A.(b)ijkˆˆˆABC⋅()×=A⋅xyz=++AAAijkˆˆˆ⋅−ijkˆˆˆBCBC−−BCBC+BC−BC(()xyz()yzzy()xzzx(()xyyx=ABCBCxyzzy−−−ABCBCyxzzx()+ABCzxy−BBCyx()()orABC⋅()×=++ABCABCABC−−−ABCABCABC(1)xyzyzxzxyxzyyxzzyxNotethat()AB×⋅=⋅()×,ordingto(1)CAB⋅()×=++CABCABCAB−−−CABCABCAB(2)xyzyzxzxyxzyyxzzyx()()Therighthandsidesof(1)and(2)⋅×=×ABC⋅.(c)ijkˆˆˆijkˆˆˆ()ˆˆˆABC××=++()AAAxyzijk×BBBxyz=xyzBCyz−−BCzyBCzxBCxyBCxy−BCyx=ABC−BC−−ABCBCABCBiˆ+−CCABCBC−−ˆjyyxy()yxzzxxz()zyzz()yxxyyx()+ABCBC−−ABC−BCkˆxzxxz()yyyzzy()ˆˆ=+()ABCyxyABCzxz−−ABCyyxAzBBCzxij++()ABCxyxABCzyz−−ABCxxyABCzzyˆ+()AxxzxBC+ABCyzy−−AxxzBCABCyyzk=+BACAC−CABAB+iˆ++BACAC−CAB+ABˆjxyyzz(()xyyzz()yxxzz()yx()xxzzˆ++BACACzxxyy−CABABzxxyy+k()()Addandsubtracttheunderlinedtermstoget1SolutionsManualOrbitalMechanicsforEngineeringStudentsChapter1ABC××()=++BACACAC−CABABAB++iˆxyyzzxxxyyzzxx()(()ˆ+++BACACACyxxzzyy−CABABAyxxzzy++Byj()()+++BACACAC−CABAB++ABkˆzxxyyzz()zxxy()yyzzˆˆˆˆˆˆ=++BBBACACAxyzijkxxyy++ABABAB−xijk++yzxx++yyzz()()()()or()()()AB××=⋅−⋅()AB×⋅()CD×=×[]()AB×CD⋅But[]()AB××CD⋅=−[]C××()ABD⋅(1)Usingthebac–cabruleontheright,yields[]()AB××CD⋅=−⋅[]ACBBCAD()−⋅()⋅or[]()AB××CD⋅=−⋅()AD()CB⋅+()BDCA⋅()⋅(2)Substituting(2)into(1)weget()AB××CD⋅=()AC⋅()BD⋅−⋅()AD()BC⋅[],vv=+×+Ωrv.(1)orelrelFromthegiveninformationwehaveˆˆˆvIJKo=−10+