| 单词 | curvilinear coordinates |
| 释义 | curvilinear coordinates Cartesian coordinates: r = xi+yj+zk, dr = dxi + dyj + dzk. Cylindrical polar coordinates: r = (r cos θ, r sin θ,z) dr = drer + rdθeθ + dzez where er = ( cos θ, sin θ, 0), eθ = (− sin θ, cos θ, 0), ez = (0, 0, 1). Spherical polar coordinates: r = (r sin θ cos φ, r sin θ sin φ, r cos θ), dr = drer + rdθeθ + r sin θdφeφ where er = ( sin θ cos φ, sin θ sin φ, cos θ), eθ = ( sin θ cos φ, sin θ sin φ, cos θ), eφ = (– sin φ, cos φ,0). Denoting the coordinates u1,u2,u3, we see in each case that dr = h1du1e1 + h2du2e2 + h3du3e3, where each hi > 0 and e1,e2,e3 is a right-handed orthonormal basis. Such coordinates are called orthogonal curvilinear coordinates, and general expressions for div, grad, and curl exist for such coordinates. (See appendix 16.) In particular the Jacobian equals h1h2h3. |
| 随便看 |
|
数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。