math214:hw13
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math214:hw13 [2020/04/29 10:24] pzhou |
math214:hw13 [2020/04/29 10:34] (current) pzhou |
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| $$ J(t) = \sum_i f_i(t) e_i(t). $$ | $$ J(t) = \sum_i f_i(t) e_i(t). $$ | ||
| Define coefficients | Define coefficients | ||
| - | $$ a_{ij}(t) = \la R(\dot \gamma(t), e_i(t)) \dot\gamma(t), | + | $$ a_{ij}(t) = \la R( e_i(t), \dot \gamma(t)) \dot\gamma(t), |
| Prove that the Jacobi equations can be written as (Thanks to Mason to point out a sign error in the original eqn) | Prove that the Jacobi equations can be written as (Thanks to Mason to point out a sign error in the original eqn) | ||
| $$ \ddot f_j(t) + \sum_{i} f_i(t) a_{ij}(t) | $$ \ddot f_j(t) + \sum_{i} f_i(t) a_{ij}(t) | ||
math214/hw13.1588181068.txt.gz · Last modified: 2020/04/29 10:24 by pzhou
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