Question

Compute in MATLAB

1. Transform the following vector into cylindrical coordinates and then evaluate it at the indicated point.

AT P3 (2, p/2, p/4)

Answer 1

solution- the vector in Spherical coordinate system. ). is given by (from question). & sine R + cose ô t (coso ² ô as Given the point, P.13,/211/4). The conversion matrix from Spherical to Cylindrical coordinate systern for a rector is given by ſ Ap] sine case oll. Aq] [ [cose -smo o ^« where, de, AO, Az are components of vector Aap + Aga + A₂6 and Ar, AE, Ac are components of rector: Agat Aa + Apa From the question, the unit vectors for spherical System are taken as (R, O , ê, which implies lêsan , ê sâo, § is fp), and the components → Ara sine, Ap = Cose, Ap = (Cosp)*
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→ The rector in cylindrical system is given by f Ap 7 [sino core off sine 1 10: 0 0 1 [l.coco [42] cosoi -sino :O) cos por [siñe + coše +ó. 7 " . Lo #o + coco Sinecos - Sinecoce to Fosfoot coco - 1) coś D . Trigonometric identity ... The given vector in cylindrical coordinate system is, Tea 1.2. t. cošo â to â 1 Now, the value of vector ē at point P3 (2, 4, 1/4) T'es ht coi (2) 9+ oa a 2. ão + 0. do 14.0.cat :
This question is based on the conversion of spherical coordinates system into cylindrical coordinate system.