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Continuum mechanics - rate of work done in reference frame - indical notation doubts
Tue, 2013-07-16 00:22 -Ashesh Sharma
Hi,
I have been stuck on this for a couple of days now. Could anyone please point out as to what am I doing wrong ?
I have seen the same derivation for the rate of work done, in the book by holzapfel but it is not in index notation.
Thank you
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po52gIkg7eKS/OuQmCG0zmXD4UzZCOYI/T3/TvE7uX8+HU1r2x0br0IJV/b/qtbqVqY0fq7G2SLlWWAo1hPN4vBN3A5B28MgK1O4nPAzXBsKfs/4qT27Wv/xOFt+Sa0VtWrOqpdA7mdq8Gc7UIiVbYSnQELvDbJ6/AUg7eDQ2BxsErHoa6aY+/qZmy+xn6Uj7DUDawcOwpAvJYNXTSDb1+MrufWQHRxwcpB32ZO0vhghY9TRSTX38jcK22U3aUfZbgLTDnuNvWIEPVj0Ns6lb29lfi622m7YLQv8g7bAHEaoBVj0NTO2x2byHrN8DpB32sChcA6x6GpgaAGmHPYc/Uw4CWPU0MDUA0g47Rt9UdA1Y9TQwNQDSDnvGfhHoKrDqaWBqAKQd9rCFtgZY9TQwNQDSDjuY89QAq54GpgZA2mFPY58DHwSsehqYGgBphx18XroGWPU0MDXAgrSDC4GxBlj1NDA1wLIg7eDwej7YgFQcrHoamBpgWRakHZb36uQ0v/9BXCwFVj0NTA2wA2mH9UcyCIvlwKqngakB9iDtAAAAQ4G0AwAADAXSDgAAMBRIOwAAwFAg7QAAAEOBtAMAAAwF0g4AADAUSDsAAMBQIO2Ds37Og+95dAuNCLcChz8O0j4y6xe1+bZ2t9CIcCtw+CIg7eNCxxgAGhFuBQ5fCKR9WOaJbFb30IhwK3D4UiDtozJPf/xwde/QiHArcPhiIO2DMk9sQekeGhFuBQ5fDqR9TN5bTBn+dg2NCLcChy8I0j4mDH8HgEaEW4HDFwRpH5L38JdO0jU0ItwKHL4kSPuQzNMfma3eoRHhVuDwJUHaR+TzMSc6Sc/QiHArcPiiIO0jQmZrAAZpxFYeY55QjbZpxVO2tFgnI0j7iLwzW106JHwZpBGvD47rB8mR9pZp0eGv995skPYB+cSyLh0SPtCIZZinx/P1MSfS3jA4fFkalvZ1sN1Sa29+k6ipem1h0UrgPSdouNV20IhFqSbtlcJUm9GvJiM4fEtB5mxp3yqjjNO0jb3ouPkMYstLdx8HS6ye0zQnPtqvOzjUaHRnB65z283dHDNc6HojNOKBepQusOqsvVKYaiz6VSbP4RU/ybfaUcdrJsicLe2Ot+4WMgRPbuqTwk1VJkReJ1kvPD2a7N96+Xp+YWO/no/tw33v4j3ut0Ne2tadNqJ720OCGi0wEIW9e9aX9kjhGW92ZQecLt8iO+jwGz/JLkkrcEnwn2aCzMnS7v6uz07L/Z/za2nY2tFHEA92kvOfUWjnGitv+1CppQB3vfMaRmjEZZmnfEMWLbCmtFvCVEb4yI5+HYWqDcccXhCOY2PKXMdrJsicK+2v52PzjNJczbFAEyH2S0vDjDDZqnjVdlA5FBXfMOtHdzkCNPG7koM0YjMFVpT2SmGqqehXn4MO7zbtIWk/5HjtBJkLt9HFY1BDGfCe9nhkd5KrRi/KfUtPP/3eJN2hka3UvTVi8RFF4QIrmqVSmGoo+qn4idZDReU0kSTEh3znmOO1E2QulPZoZ1tPiLyZqmxK+B3+HAqUEtrWIOz8k2ut7ZkoVhMjJTtJ+BYms0TRHOHwtN3dUzb5oVJ44la2R/beiEcy8UULFJ5Ssc63/pdV4gpayGxMBUOXrv9ArucpiX6yQ/rneptTCjg5SU7S67Dq+l4paSocic6XrNB5jppj87JPp1q/g0MxSvcZlyb5dsg3675/b9vVa0E/zZ6C+/8xflv4ZrEydxHZRytOktiJUbtqhgVyKr9rpazLt6ts9JkwT21K2nl9t2Ix2clxQu039S5j++Ewg6hWJiSXdy9mzSGiEY/9RmkKOka87g1C07Zl2MOL+w9V58u1kNSHO/EIJPOZdJuTMeHPdIrxF+fijS1oQT51n5NY2/tlamJgcz9KJahhPekBUKudt8jayDRgLy9hTMia2Vxs69GlBIAhyxZvMCU2+7CsOBJ/hlB4ZS6stcKbrmWYvVHkO61e4aU9q4yeJXvkeiG6X4SEZ6EAhsPMpdJezQG+U2wv8Q/QxN/s5xqHShUW9FX/AsK1cTAkU4SvEgdrxyRBdW0+ZN2qUXklcvtzRtZZP/QYSO6MlQgHV+yQBti9s211y4/Gw9Tutjb04BisYELxdRmUd9+PR9lC8xz+OJbKMyO13yQuUrao9EkXdlF3wg2vamEWCliJxUOlqmJgWhKylQDAclx/aChJhvkPFQkHe9FUUPJUpHKtZtGaWWR/U1fjSjNQPWaexNS7RRrgQVxeunbJRyL7RXNJMG+zWPhL1vZtc134j6CAxTvLXkOX1vZdcdrP8hcJO3GdHxoFutnToTiDHoaKUG6dfwW/sEyNbFQq5NIZyhDGKkcZbyq3FfKcRhLlnxLk6rf3Y9MC2ukK7tqROMC/64agfODBRpGBpZ7hO48zcuq4hux9Keq0TAlnRM3mKVY24X7m6Y7lVJU4SRKlsMX2jSwL9DwaKcHmXQuknZjOn6/Hhg8YCkl4a/G2uoJsFhOLqcmFj6dJM2HDCk7YT5wZDk8eN8jGUQtuErFfc59NrTI/qa/RkypaizGxQq0qHZe6vPnPGsVfxFbyEFbopLtUHKxtgvlE7LS3oUHr3LFMhy++KTdUmAHQeYaaY/GIN9ypnHs6/mwT5VNJcRLUSboKQsDtppYR5Q5ncRStq8K+5y5NvL+Hjem44Xwk1KyV+Y8PR5Kfjkwk9mEswvy9D01Yqg3y6WteUlpNTsaHmrOft4ddZo2d3gPJJ5CLtUQpvTMrf6AlmKNF/oZ5cNyWMf6OQ6fNQEI9RJ7gYWCzFIxzlwi7fGV5JCQz9uXyTaF+EP5mBfHS5DOCtdVHhaXqIlV2j/WTe8kpnmQ4UFTF9r9qK6ltWwlOx10nr7LpV+nEYZhwebKSuwepaNGjPVmuYEc4ZSGxpEeFxgZBEYhcYRr9RWAxDA1/3bgCcqw+a+l2EDlnfP2ZTWq7DkOH5cRiUAYTSnweJBZKseZ86XdSe4kZLl/13l5Kq0se8o+WBtDZ4g9U5GaJC23pXm8ebTqbgrwL9CyoNJxJcun1CKl5G0133/63WtvWCFBvT+Wl9k9SJeNKHYS/6pVHIRoZggPkZGBf04KQuTX1lCNYUqZtLnu76eo4tFPrf32PLexU33KxxmDFCTV4S0yIqJJe3KBx4KMf7h0nGn499ob4ciyb/F6WKqRrgrllvq1jn98RFqv5FiJnUh7q43ol3YwBRkcGWzOaaDPjkctZc+cgvdM7TiDtEcousMtn2Aezjs1bSBbVhS06c1xZa9TsnQnLzN0UUJ+gEbU0/G5ocwyMrhkEQUOkOzwvVM9ziDtYRpR9gRS96NYl/CtRVmT5o2U7LFThWuUfZhGlNPx7yN5JVpGBjX32UENsjbId031OIO0BzFnwdvB/HpLeONmDpuo620jKTNpL1+yfq/vv6+IN8M0olfaVpF/vWue0gYxkZEB6fjuMDv8ONSOM0i7Rq+LPxd2EmVncoHxUb2SJTYp34umEcM0oleaM0LQXrSLlBcbGZCO744bSnvtOIO0j0Zzi1b15lDjzs5u1IhpWEYGHababk9zDt8/SPtotLKj/0u9KdTAk7P7NGJ5WhmFQAKtOfwAIO2DUXBD1VH0T320W3Ib3KIRK9HTKAQ+NOTww4C0D0Z/W/rBg0bMobtRCHzB4cuDtA/GVXu6oSA0ItwKHL48SPtYMPwdABoRbgUOXwGkfSzYHTwANCLcChy+Akj7ULA7eABoRLgVOHwNkPaRoI8MAI0ItwKHrwLSPhB8OnsAaES4FTh8HZD27vn9zmLCr8NBY9CIcCtw+Nog7b2z/kAIPaRbaES4FTh8dZB2AACAoUDaAQAAhgJpBwAAGAqkHQAAYCiQdgAAgKFA2gEAAIYCaQcAABgKpB0AAGAokHYA6Infh8wAQANpB4A+WL9hhrQDBEHaAaAH5unxfPFDYQAWkHYA6AikHSAO0g5QgHn6k2j0xy/WzHb95LZimex7I+0AcZB2gDK8NWwj5h9Ra1OGPpU7ZezhWWbZKXRA/j3rIe0AcZB2gDLMk6dfb8lqUofOrJpgmfwf6kbaAeIg7QBFeCe5Xc1pV9rftT1nvUCyzMHSWjQpQEMg7QAlkPTrTP1MRJxI16GwFU6sOUC3IO0AJVDT8U2qUGQi7WyzO7oncG+ZQ5n4w7vwAG4B0g5QgNfz4ejXV4dKik9wr3mSAgcm0s7ev9fzcXhoshtFkE8HOAGkHeA40jS3yen6Gy2p7e0NOC7EnVkGYAyQdoDj9LUArKTjhYc4vgNuN1ookQcAgBhIO8BhTMq+y9l/0+vnJ6eVdPw8+bXxt/jvVx6cU/3jXgHzRDoeoDpIO8BRbHNbX/tkNQwWUGKtXR6ISEeFQYBWZzl1H9wdbx3cJJoJAJB2gMNkpuMvSk4rL9sLk/bPOvmBWXbMMhbVZuMdQDJIO8BB4h+mkffLrz88/ttrdoLSaxNpX9r3L+9pu/6/xw3peKEuzMcByoO0AxzD9qn4SDr+vH146p3cVXR5xq7NskML7QHLxAY3+qABAEIg7QAHcNa/AwrkZ5XXGeupa8nBibT7ppp/kpYbl44bLGMZ3LDQDpAB0g5wAuv8dHtE1dBqHHubzX+K9fiRvQb69Sy0A+SAtAPUR0/Hn6tdx5VdS+VnzKwtgxsm7QA5IO0A1ZHT8e8jJ2r7wR9qSUnHG7AMbthnB5AF0g5QnY2KvYVqK2e/renzVEvF1jX0ox+Wc55idzyjTpHBDel4gDyQdoDqeDu9HTWs8VMyNVD2q0tfsTMWFhvckI4HyANpB4ADHEzHr2XIr9o1P+ABaBGkHQDyqTixJh0PkAvSDgA51P59G7LxANkg7QDQFtf9KB7AICDtAAAAQ4G0AwAADAXSDgAAMBRIOwAAwFAg7QAAAEOBtAMAAAwF0g4AADAUSDvA4Kw/DsMnYCqDqaERkHaAkVl/FpUfSK0MpoZ2QNoBxgWNOQ1MDS2BtAMMC59hPw1MDU2BtAOMCj+KehqYGtoCaQcYlHliN9dJYGpoDKQdYEzeu7WZSZ4ApobWQNoBxoSZ5GlgamgNpB1gSN4zSfTmBDA1NAfSDjAk8/RHkvgcMDU0B9IOMCKf76KhN/XB1NAeSDvAiJAkPo0WTd1ineBMkHaAEXkniYntJ9CiqZH2u4O0AwzIJ0lMbK8PpoYGQdqhMd5zoMZj5foLX42usI6w/tuFJ2BqaBKkvUc2Px3pxRT/Fdtft+0mAEk7jp2nWLkuFLWd8vyY6+rmllvNbjTHE5zCNmU43eH8BskzdXF/Vgo0d/seTA12kPZO+faxXZ+Vk4PKyc3yej6kwOGtaV46X2r7C2SNSPvij9OSnHHnCd9rPd/4StEVz5ttas+fjzaatOj/ej5sJfZgarCDtPeK+C7tt9uJ0l61Lxb9eQylMOGbXxdOneUvkLXyMyGNSbvUapZm25tTG8wpg8FTOCbtbqWPvSEvuuQ82QzTg6nBDtLeK4Jcv56Pv8c0eT3PPHDPp6iiKfWVBijXSbsc4VpR9na2dsnDSuOmct8TZO278hdVs00tWeaQtB8awfdgakgAae8Vvx/P09/fNMtr7XU7Y2GBlSssBq7LvgMm1qawHV7PR25Z7Ui78nl1W8P5niBdd8LQNUCuqYuPVI95Xw+mhgSQ9l7ZR4bX8/H3eL68UBrsjM6umGneJu9+f/oekDfRSpt3vOgS23zjVmMqkI4P39Gr9Ptu2rZ3SZ32x0x2SCZ7VHZE2t1NmtFmC99D++EUZdoe9QRBEN9D2rRnLEiuqdV0vFJS1NqCS4Yq1aGpIQGkvVd2Pf3X6XYdXO+Mu7U0Z3fTNyp8s86/UgLpVaXLu+HKj2dyNQzpeHWJM3JHt7K/Yp1H9rIhtt0LFdLxmUV+jJOqN45Nv4NFFYO0qzliYUpo8gTRDayPGdxEHhzFxAtNNfV+QSe6uzBm7Z1lLEP6iqaGq0Hau8VRnHWE7hzWo7MfWtUE4ePx8JVQrcniXe8FMG+yGxPSZY18W6TAZbvj7obB++uJU1HZi8e+rBXUnK1dXltJIZUAAARqSURBVFvEsq8GaddM4ouJ0RN294wOP+qTt4tO8ufwg0SsnVBgt6aGBJD2btl0x9fz8eupu8NyyJHChL6TeR+Arfvv/btIMwupGpF0vBrloneMLvLaJu2BUGgO8XLeWycprKbrjdr8R7IQ6mBHfiPO4gnbIptY+T3wWntJpdxZVBfijk0NCSDt3bJ2PGdRzTkczMVLE/SIgtlnsIsfQ7wYaK3G4kuBLNDRO26PypFPmtTbBjPHhVAmp9xodtdDCu6H9yhG0vGrVVM94X24iZXfdFMvS31l95JRPzo2NaSAtHfLt+PtxufK4S3SuN3U45PS8f6sVBRIoRqG3fHivD16R+HM2MNcnY7PW2tP1ht9AHPkicKLK+E5u+IJa5kZCeIaa+1Z0l58GGhuq7NMDVeDtHfLp0M+J2GW+X4HLryJJvoO65ENZaE/JFZDvrGtwkGEzUPynjvTYKbKpD1341Lyrm1hBKFuaDSjtKZpm4eaMfic+2xFbZJNvSy1Ju2WAns2NaSAtHfLb+YpvUATjMnC+vPjYUjHi/HDPfh6/rbcKfPdQBZWrsYiBx91i3Xgjvsk5f6B9gXIFbJM2jd2yOeV/V57AWkPvoi1vUtkY5e4bBEbk6meEEi4XESOtGetdISsbS+wnKk3KZA2WgIckPZuUTKBlndxnEgwT3/bD9389ESZKX9P2lz+K8tZ9BeEMjTz1qqxPpIkB+FVhd0d908UesJPhdZc5frIm7tsHli3wwWkv5DlJmVtM/awtPt/1Wtl9YRNKa3ISbqpD+2p1zeIGAssYmqn5+SmlqAqSHu3KF3dNoDfLEv/1OjPiVHSnMs7SSxKvk1sPV6phrs+KgjF7rahO/pr8aEKaxXaHlTufLnsZImHax7DtXGx2RPLJMUM/vD5Rb+kWpq1Z9jaNZOLvCwqXeH2TzfJEg7wHA0NrMdmfuZej9LR9qbBGkHGA7DQjmU4Xam3k/ltf31cC1IO8BoZO3ahhzuZ+rdpB1lbxSkHWA0jr+3BkZuaOqtttf5mAMUAGkHGI0b6s1V3NLUm517yHqrIO0Ao3G79d/rwNTQJkg7wGgc/vg7WMHU0CZIO8BgHP/4OxjB1NAoSDvAYNT6DTrwwNTQKEg7wGCwbfk0MDU0CtIOMBbMJE8DU0OrIO0AY9HYR9ZHBlNDqyDtAEPBJ71PA1NDsyDtACOB3JwGpoZ2QdoBBuL1fLCt6xwwNTQM0g7QPfP0mT7OE2pTF0wNXYC0A/TO50PmvIdVH0wNfYC0AwAADAXSDgAAMBRIOwAAwFAg7QAAAEOBtAMAAAwF0g4AADAUSDsAAMBQIO0AAABDgbQDAAAMBdIOAAAwFEg7AADAUCDtAAAAQ4G0AwAADAXSDgAAMBRIOwAAwFAg7QAAAEOBtAMAAAwF0g4AADAUSDsAAMBQIO0AAABDgbQDAAAMBdIOAAAwFEg7AADAUCDtAAAAQ4G0AwAADAXSDgAAMBRIOwAAwFAg7QAAAEOBtAMAAAzF/wOfxcbCnoIlaAAAAABJRU5ErkJggg==)
Your result is correct
Hi,
Your indices notation is correct. You have got the result.
Best regards,
- Ramadas
Thanks a lot. I was having
Thanks a lot. I was having some trouble with indical notations. Hopefully that is resolved.