Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 2.2, Problem 2E
Interpretation Introduction
Interpretation:
Analyze
Concept Introduction:
For a flow, equation is represented by
Fixed points are those points where
When vector field for flow is represented on the real line, among these fixed points, the points where the flow is towards them are called stable points, and the points where the flow is away from them are called unstable points.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen
seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate.
(a) Determine the position function s and the velocity function v (for all times t).
4512
if 0 sts 3
405
if 3 26
15r3
if 0 sts 3
405
if 3 26
Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the line y = x-1 at (1,0).
Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy
Chapter 2 Solutions
Nonlinear Dynamics and Chaos
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5E
Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.7 - Prob. 1ECh. 2.7 - Prob. 2ECh. 2.7 - Prob. 3ECh. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - Prob. 6ECh. 2.7 - Prob. 7ECh. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 8ECh. 2.8 - Prob. 9E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.arrow_forwardA steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128/257 feet. The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second.The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)arrow_forwardFind the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) = √√3ti + e4j + 6e¯¹k at t = 0. (Use symbolic notation and fractions where needed. Give your answers in the form (*,*,*).) v(0) : = a(0) = (Use symbolic notation and fractions where needed. Give your answers in the form (*,*,*). Use t for the parameter that takes all real values.) l(t): =arrow_forward
- Determine an equation of the tangent line to y = (e3x - 2)4 at the point (0,1) then solve for y.arrow_forwardA mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv ' dt exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.arrow_forwardThe equation of motion of a particle is s = t* - 4t3 + t- - t, where s is in meters and t is in seconds. (Assume t > 0.) (a) Find the velocity, v(t), and acceleration, a(t), as functions of t. v(t) a(t) (b) Find the acceleration (in m/s2) after 1.2 s. a(1.2) = m/s? (c) Graph the position, velocity, and acceleration functions on the same screen. y y a a 1 3 4 3 4 -5 -5 - 10 - 10 - 15 -15 - 20 - 20 y y S a V IIarrow_forward
- help me pleasearrow_forwardA particle's position with respect to time as it moves along a coordinate axis is given by the function p(t) = t³ + 3t² + 3t + 1. What is the particle's acceleration at time t = -3? Do not include "a(-3) =" in your answer.arrow_forwardFind an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at (1, 0)arrow_forward
- A projectile is fired straight up from a platform 10ft above the ground, with an initial velocity of 160 ft/sec. Assume that the only force affecting the motion of the projectile during its flight is from gravity, which produces a downward acceleration of 32 ft/sec?. What is the equation for the height of the projectile above the ground as a function of time t if t = 0 when the projectile is fired? s = -16t2 + 80t + 10 s = 16t2 – 160t + 10 - O D A s = -16t2 – 160t + 10 s = -16t2 + 160t + 10 Barrow_forwardThe equation of motion of a particle is s = t4 - 3t3 + t2 - t, where s is in meters and t is in seconds. (Assume t 2 0.) (a) Find the velocity, v(t), and acceleration, a(t), as functions of t. v(t) a(t) (b) Find the acceleration (in m/s2) after 1.1 s. a(1.1) = m/s2arrow_forward(3) Suppose that the position function of a particle moving on a coordinate line is given by s(t) = ³-2t² + 3t - 7 in meters, where t is in seconds. (a) Find the velocity and acceleration functions; (b) Analyze the direction of the motion that shows when the particle is stopped, when it is moving forward and/or backward; (c) Analyze the change of speed that shows when it is speeding up and/or slowing down; (d) Find the total distance traveled by the particle from time t = 0 to t = 6 seconds.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY