Show that the helix [a cos t, a sin t, ct] can be represented by [a cos

Question:

Show that the helix [a cos t, a sin t, ct] can be represented by [a cos (s/K), a sin (s/K), cs/K], where K = √a2 + c2 and s is the arc length. Show that it has constant curvature k = a/K2 and torsion τ = c/K2.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Control Systems

ISBN: 978-0136024583

12th edition

Authors: Richard C. Dorf, Robert H. Bishop

See More Books

Question Posted: Nov 05, 2010 09:16 AM

See More Questions

A satellite single-axis attitude control system can be represented by the block diagram in Figure CP2.5. The variables k, a, and b are controller parameters, and J is the spacecraft moment of...
Show that any positive number M can be represented by (1 + x) / (1 - x), where x lies within the interval of convergence of the series of Problem 11. Hence conclude that the natural logarithm of any...
A linear dynamical system can be represented by the equations Dx / dt = A(t)x(t) + B(t)u(t), y(t) = C(t)x(t) + D(t)u(t), where A is an n n variable matrix, B is an n r variable matrix, C is an m n...
A job order cost accounting system is fully integrated into the general ledger of a company. Identify the major general ledger accounts used in a job order cost system. Explain how manufacturing...
Let's look at Dick's Sporting Goods (Dick's) some more. Think about Dick's. Think about accountants reporting what Dick's has, where it got its money, and what it has been doing to create value. Is...
The global recession forced thousands of firms into bankruptcy. Does this fact alone confirm that external factors are more important than internal factors in strategic planning? Discuss.
Air enters a 0.5 -ft inside diameter duct with \(p_{1}=20\) psia, \(T_{1}=80^{\circ} \mathrm{F}\), and \(V_{1}=200 \mathrm{ft} / \mathrm{s}\). What frictionless heat addition rate in Btu/s is...
Whirlpool Corporation conducted an activity-based costing study of its Evansville, Indiana, plant in order to identify its most profitable products. Assume that we select three representative...
what is developmental psychology (or developmental science)? What do developmental psychologists/scientists do? What is the benefit of developmental psychology/science? Why study developmental...
A northwestern distribution company surveyed 53 of its midlevel managers. The survey obtained the ages of these managers, which later were organized into the frequency distribution shown. Determine...
Show that if C is represented by r(t) with arbitrary parameter t, then assuming k > 0 asbefore. (23***) T(1) (r' r')(r" r") (r' r")
Show that u' = p, p' = u + b, b' = p.
Smoothing the Business Cycle versus Fostering Economic Growth: Psychology Meets Normative Macroeconomics: It is sometimes argued that there is a policy trade-off between softening the impact of...
Why is Internet fraud particularly difficult to police? 1. More people are online feeding leads to police. 2. Con artists are more convincing online than they are when operating in person. 3. Nearly...
Which of the following is not true with regard to evidence? 1. Evidence is anything legally admitted at trial. 2. Evidence is anything perceivable by the five senses: sight, hearing, touch, smell,...
What is the cause of Down syndrome?
Which of the following is not associated with increased risk regarding insider cyber fraud? 1. Supervisors can implement strict controls over information system personnel. 2. Insiders are often aware...
Which of the following attributes of a fraud examination often provides the most compelling evidence of intent on the part of a fraudster? 1. Perceived pressure 2. The fraud act 3. Conversion 4....
In an elastic collision between a lightweight object and a heavy object, which one carries away more of the kinetic energy? Does the answer depend on the initial speeds? (Begin with the zero-momentum...
Derive Eq. (18.33) from Eq. (18.32).
In the setting of Exercise 68, show that the point of tangency is the midpoint of the segment of L lying in the first quadrant. Data From Exercise 68 Let L be the tangent line to the hyperbola xy = 1...
Consider a hedonic pricing model for educational attainment. Would isoprofit curves for the firm be upward or downward sloping? Explain. Question 2 (Mandatory) (3 points) Listen For workers, would...
6. Determine the sum of the measures of the interior angles of this polygon.
Consider the perfectly competitive Corn industry. It is initially in long run equilibrium at quantity Q0 and price P0. a) Draw a supply and demand diagram for the Corn market showing this...

Show that the helix [a cos t, a sin t, ct] can be represented by [a cos

Question:

Step by Step Answer:

From rt a cos t a sin t ct we obtain r a sint a cost c rr a c ...View the full answer

Modern Control Systems

Students also viewed these Calculus questions