EBK ENGINEERING MECHANICS: DYNAMICS, SI
8th Edition
ISBN: 9781119047315
Author: Bolton
Publisher: VST
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Chapter 7.11, Problem 105P
To determine
The gyroscopic moment
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3.) 13.152* - A sphere (m = 2 kg) is connected to a fixed point O by an inextensible cord (L = 1.2 m). The
sphere rests on a frictionless horizontal surface at a distance of x = 0.5 m from O when it is given a velocity
(V.) in a direction perpendicular to OA. It moves freely until it reach A', when the cord becomes taut. Find
the maximum possible velocity v. if the impulse of the force exerted on the cord is not to exceed F = 3Ns.
4.) 13.165* - Two billiard balls A & B (same mass m & diameter d = 2.37") are as shown. Ball A has velocity
V₁ = 3 ft/s when it strikes B, which is at rest. B then moves in the x direction after impact. Find (a) angle 0,
(b) the velocity of B after impact (VB'). Positional variables are x = 6" and y = 10", and e = 0.9.
We will consider a linear system and a nonlinear system under uncertainty, each expressed in the form
of a set of stochastic differential equation (SDE) as follows:
=
da (Ax+ Bu)dt + Gdw,
dx = f(x,u,t)dt+Gdw,
(1)
(2)
where x is the state, u is the control, and dw is a differential increment of standard Brownian motion, i.e.,
E[dw] = 0 and E [dw(t)dw(t)] = dt-1.
In this problem, we consider the linear SDE, Eq. (1), with a very simple model where x = R², u = [0,0]
(no control), and dw R². The matrices A, B, and G are given as follows:
A=02x2, B=02x2; G = [000]
(3)
where σp Є R represents the degree of the uncertainty, and let us take σ₁ = 2 and σ2 = 3. Assume that the
initial state is deterministic and e(t = 0) = [0,0]. Take the following steps to simulate the given SDE for
1 € [0, 1]:
(a): Consider the increments of w between each time interval [+1). Derive the analytical expression
of Aw using w~N(02, 12), where Aw, w(tk+1) — w(tk).
(c): Derive the approximate continuous-time EoM from…
Chapter 7 Solutions
EBK ENGINEERING MECHANICS: DYNAMICS, SI
Ch. 7.5 - Place your textbook on your desk, with fixed axes...Ch. 7.5 - Repeat the experiment of Prob. 7/1 but use a small...Ch. 7.5 - Prob. 3PCh. 7.5 - A timing mechanism consists of the rotating...Ch. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10P
Ch. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - In manipulating the dumbbell, the jaws of the...Ch. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - For the robot of Prob. 7/16, determine the angular...Ch. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - The circular disk of 120-mm radius rotates about...Ch. 7.5 - Prob. 21PCh. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - The pendulum oscillates about the x-axis according...Ch. 7.5 - Prob. 28PCh. 7.6 - Prob. 29PCh. 7.6 - Prob. 30PCh. 7.6 - Prob. 31PCh. 7.6 - Prob. 32PCh. 7.6 - Prob. 33PCh. 7.6 - Prob. 34PCh. 7.6 - Prob. 35PCh. 7.6 - Prob. 36PCh. 7.6 - Prob. 37PCh. 7.6 - Prob. 38PCh. 7.6 - Prob. 39PCh. 7.6 - Prob. 40PCh. 7.6 - Prob. 41PCh. 7.6 - Prob. 42PCh. 7.6 - Prob. 43PCh. 7.6 - Prob. 44PCh. 7.6 - Prob. 45PCh. 7.6 - Prob. 46PCh. 7.6 - The center O of the spacecraft is moving through...Ch. 7.6 - Prob. 48PCh. 7.6 - Prob. 49PCh. 7.6 - Prob. 50PCh. 7.6 - Prob. 51PCh. 7.6 - Prob. 52PCh. 7.8 - Prob. 53PCh. 7.8 - Prob. 54PCh. 7.8 - The aircraft landing gear viewed from the front is...Ch. 7.8 - Prob. 56PCh. 7.8 - Prob. 57PCh. 7.8 - Prob. 58PCh. 7.8 - Prob. 59PCh. 7.8 - Prob. 60PCh. 7.8 - Prob. 61PCh. 7.8 - Prob. 62PCh. 7.8 - Prob. 63PCh. 7.8 - Prob. 64PCh. 7.8 - Prob. 65PCh. 7.8 - Prob. 66PCh. 7.8 - Prob. 67PCh. 7.8 - Prob. 68PCh. 7.8 - Prob. 69PCh. 7.8 - Prob. 70PCh. 7.8 - The assembly, consisting of the solid sphere of...Ch. 7.8 - Prob. 72PCh. 7.10 - Prob. 73PCh. 7.10 - The slender shaft carries two offset particles,...Ch. 7.10 - Prob. 75PCh. 7.10 - Prob. 76PCh. 7.10 - Prob. 77PCh. 7.10 - Prob. 78PCh. 7.10 - Prob. 79PCh. 7.10 - Prob. 80PCh. 7.10 - Prob. 81PCh. 7.10 - Prob. 82PCh. 7.10 - Prob. 83PCh. 7.10 - Prob. 84PCh. 7.10 - Prob. 85PCh. 7.10 - Prob. 86PCh. 7.10 - The thin circular disk of mass m and radius R is...Ch. 7.10 - Prob. 88PCh. 7.10 - Prob. 89PCh. 7.10 - Prob. 90PCh. 7.10 - Prob. 91PCh. 7.10 - Prob. 92PCh. 7.10 - Prob. 93PCh. 7.10 - Prob. 94PCh. 7.11 - Prob. 95PCh. 7.11 - Prob. 96PCh. 7.11 - Prob. 97PCh. 7.11 - The 50-kg wheel is a solid circular disk which...Ch. 7.11 - The special-purpose fan is mounted as shown. The...Ch. 7.11 - Prob. 100PCh. 7.11 - Prob. 101PCh. 7.11 - Prob. 102PCh. 7.11 - Prob. 103PCh. 7.11 - Prob. 104PCh. 7.11 - Prob. 105PCh. 7.11 - Prob. 106PCh. 7.11 - Prob. 107PCh. 7.11 - Prob. 108PCh. 7.11 - Prob. 109PCh. 7.11 - Prob. 110PCh. 7.11 - Prob. 111PCh. 7.11 - Prob. 112PCh. 7.11 - Prob. 113PCh. 7.11 - Prob. 114PCh. 7.11 - Prob. 115PCh. 7.11 - Prob. 116PCh. 7.11 - Prob. 117PCh. 7.11 - Prob. 118PCh. 7.11 - Prob. 119PCh. 7.11 - Prob. 120PCh. 7.11 - Prob. 121PCh. 7.11 - The uniform slender bar of mass m and length l is...Ch. 7.11 - Prob. 123PCh. 7.11 - Prob. 124PCh. 7.11 - Prob. 125PCh. 7.11 - Prob. 126PCh. 7.12 - Prob. 127RPCh. 7.12 - The solid cube of mass m and side a revolves about...Ch. 7.12 - Prob. 129RPCh. 7.12 - Prob. 130RPCh. 7.12 - Prob. 132RPCh. 7.12 - The solid cone of mass m, base radius r, and...Ch. 7.12 - Prob. 135RPCh. 7.12 - Prob. 136RPCh. 7.12 - Prob. 137RPCh. 7.12 - Prob. 138RPCh. 7.12 - Prob. 139RPCh. 7.12 - Prob. 140RPCh. 7.12 - Prob. 141RPCh. 7.12 - Prob. 142RPCh. 7.12 - Prob. 143RPCh. 7.12 - Prob. 144RPCh. 7.12 - Prob. 145RPCh. 7.12 - Prob. 146RP
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