/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q15P Let x=u+v,y=v. Find ds, the a ve... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q15P (page 525)

Let x=u+v,y=v. Find ds, the a vectors, and dS2for the u, v coordinate system and show that it is not an orthogonal system. Hint: Show that the vectors are not orthogonal, and that dS2contains du dv terms. Write the gij matrix and observe that it is symmetric but not diagonal. Sketch the linesu,v=const and observe that they are not perpendicular to each other.

Short Answer

Expert verified

The statement has been proven and the value of matrix is g=1112.

Step by step solution

01

Given Information

The given values are mentioned below.

x=u+vy=v

02

Definition of cylindrical coordinates.

The coordinate system primarily utilized in three-dimensional systems is the cylindrical coordinates of the system. The cylindrical coordinate system is used to find the surface area in three-dimensional space.

03

Prove the statement and find the matrices.

The given values are mentioned below.

x=u+vy=v

The position vector is given by s=(u+v)e铃�x+ve铃�y.

Find the value of ai.

au=e铃�xav=e铃�x+e铃�y

Find the value of metric tensor

gij=ai.ajg=1112

Find the value of ds2

ds2=gijdqidqj=duu+2dudv+2dv2

The statement has been proven and the value of matrix is g=1112.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Parabolic cylinder.

XiAij=Bj.

Show that, in polar coordinates, the胃contravariant component of dsis which is unitless, the d胃physical component of ds is rd胃which has units of length, and the胃covariant component of ds isr2d胃which has units role="math" localid="1659265070715" (length)2 .

In(7.9)we have written the first row of elements in the inertia matrix. Write the formulas for the other6elements and compare with Section 4.

Bipolar cylinder coordinates u,v,z.

x=asinhucoshu+cosvy=asinvcoshu+cosv
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Thermodynamics

Read Explanation

Linear Momentum

Read Explanation

Torque and Rotational Motion

Read Explanation

Electromagnetism

Read Explanation

Fundamentals of Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.