第三讲曲线坐标系中单位矢量对坐标的表达式

1、1.6 曲线坐标系中单位矢量对坐标的表达式曲线坐标系中单位矢量对坐标的表达式1 证明：证明：1212121eqhhqe1q2q3q1e2e3exyzrzzr,re证：证：122ee0122212qeeeqe111ee0212eqe0121eqe1）2） 0221121ehehqrqr0213qrqrq023123221qrqqrqqrqr1e2e3e0212eqe0121eqe021qrqr023123221qrqqrqqrqr031qrqr032122321qrqqrqqrqr032qrqr031221322qrqqrqqrqr0312223123221qrqqrqrqqrqqrqr解得：解

2、得：0122333112232211qehehqehehqeheh02122123312233hqeeqhehqeheh021233hqeeh0123qee0213qee1e2e3e0212eqe0121eqe0123qee0213qee2112122qrqqrqqqr221112ehqehq122122211211qheqehqheqeh0122211122211qehqheqheqeh0122211qheqeh0122211qehqhe2121211eqhhqe1212121eqhhqe3131311eqhhqe1313131eqhhqe3232321eqhhqe2323231eqhhqe

3、3）1e2e3e2121211eqhhqe1212121eqhhqe3131311eqhhqe1313131eqhhqe3232321eqhhqe2323231eqhhqe321eeeeeqeeeqqe131323121211eqhheeeqhh3313221211eqhheqhh作业作业10 求：求：3322qeqe、作业作业11 写出柱坐标、球坐标写出柱坐标、球坐标下的这九个偏导数下的这九个偏导数zr, rxyzrzxyzrr1e2e3eba 2 求：求：解：解： 322211 ebebebaba332211332211 eabeabeabebaebaeba131

4、3321221111111eqbhaqbhaqbhaeba3133212211111 qehaqehaqehaea31313321212233132212111111eqhhhaeqhhhaeqhheqhhha2121211eqhhqe3131311eqhhqe331322121111eqhheqhhqe33111333122111222111eqhaqhahheqhaqhahh332211332211 eabeabeabebaebaebaba1313321221111111eqbhaqbhaqbhaeba331113331221112221111 eqhaqhahheqhaqhahhea33

5、2223332112221112211 eqhaqhahheqhaqhahhea113331113223332223311 eqhaqhahheqhaqhahhea 22333222332111222112eqhaqhahhbqhaqhahhbba 11333111331222111221eqhaqhahhbqhaqhahhbbaba 33222333223111333113eqhaqhahhbqhaqhahhbbaa3 求：求：解：解：aaa)(333222111111eqheqheqh3213231213213211qhhaqhhaqhhahhha3322113213322113211ah

6、ahahqqqehehehhhha1a32132312132132111111)(qhhaqhhaqhhahhhqha1111222131333113123222333213213322113211qahqahhhhqahqahhhhqahqahhhhqqqehehehhhhaa3 求：求：解：解：aaa)(1a32132312132132111111)(qhhaqhhaqhhahhhqha1111222131333113123222333213213322113211qahqahhhhqahqahhhhqahqahhhhqqqehehehhhha13331131231111222132321

7、1qahqahhhhqqahqahhhhqhha32132312132132111111qhhaqhhaqhhahhhqha13331131231111222132321qahqahhhhqqahqahhhhqhh4 求：求：解：解：333222111111eqheqheqh3213231213213211qhhaqhhaqhhahhha3322113213322113211ahahahqqqehehehhhha3213323122132113211111qhhqhqhhqhqhhqhhhh作业作业13 写出柱坐标、球坐标写出柱坐标、球坐标下的下的zr, ra作业作业12 写出柱坐标、球坐标写出柱坐标、球坐标下的下的1.7 张量表示法张量表示法1 下标：下标：iaa 替换：替换：ixix2 求和：求和：bababaiiiii31adivxaaii2 求和：求和：3 置换符号：置换符号：ijkijk011123kjijkbabajkijkxbb4 符号：符号：ij01ji ji ijijaa ksjtktjsistijk5 应用：应用：aaaaa22tkkstjijkcbacba2121211eqhhqe3131311eqhhqe332211332211 eabeabeabebaebaebaba1313321221111111eqbhaqbha