VECTOR MECHANICS FOR ENGINEERS: STATICS
12th Edition
ISBN: 9781259977121
Author: BEER
Publisher: MCG
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Textbook Question
Chapter 4.2, Problem 4.74P
Determine the reactions at A and D when β = 60°.
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(b): Let us first consider controlling the orbit of deputy spacecraft to rendezvous with chief spacecraft.
Define x = [r] and x = x = R to represent the deputy orbital state and its target (= chief
orbit) in Cartesian coordinates, respectively. The control input is thruster acceleration, u € R³, in the
ECI frame. Denote the relative state by dx = x-x. Table 2 summarize the initial orbital elements.
Table 2: Keplerian orbital elements at epoch (t = 0) for deputy and chief about Earth (ECI frame)
Orbital element
Deputy
Unit
Chief
semi-major axis
ad =
11500
ac 10000 km
eccentricity
inclination
ed = 0.15
id=35
ee = 0.3
i = 50
degree
right ascension of ascending node d = 50
Ως = 50
degree
argument of periapsis
true anomaly at epoch
Wd
Vd= 0
=
40
We =
40
degree
Ve=0
degree
(b.1): Derive the error dynamics of our system in ECI frame under the influence of u.
(b.2): Consider a candidate Lyapunov function V = ½dr¹ K₁dr+dv₁dv, where K₁ = K, and K, > 0.
Discuss the positive definiteness of V, and…
One image show problem c.1 and c.2 that I need help with. The second image shows the lyapunov function and its derivative but it is NOT the same function that is given in problem. I have attached that image as an example.
This is a tilt and rotation question. Here are notes attached for reference.
Chapter 4 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
Ch. 4.1 - Two crates, each of mass 350 kg, are placed as...Ch. 4.1 - A lever AB is hinged at C and attached to a...Ch. 4.1 - A light rod AD is supported by frictionless pegs...Ch. 4.1 - A tension of 20 N is maintained in a tape as it...Ch. 4.1 - A gardener uses a 60 N wheelbarrow to transport a...Ch. 4.1 - The gardener of Prob. 4.1 wishes to transport a...Ch. 4.1 - A 2100-lb tractor is used to lift 900 lb of grave....Ch. 4.1 - For the beam and loading shown, determine (a) the...Ch. 4.1 - A load of lumber of weight W = 25 kN is being...Ch. 4.1 - A load of lumber of weight W = 25 kN is being...
Ch. 4.1 - A hand truck is used to move a compressed-air...Ch. 4.1 - Two external shafts of a gearbox are subject to...Ch. 4.1 - Three loads are applied as shown to a light beam...Ch. 4.1 - The 10-m beam AB rests upon, but is not attached...Ch. 4.1 - The maximum allowable value of each of the...Ch. 4.1 - For the beam of Sample Prob. 4.2, determine the...Ch. 4.1 - The maximum allowable value of each of the...Ch. 4.1 - For the beam and loading shown, determine the...Ch. 4.1 - PROBLEM 4.15 The required tension in cable AB is...Ch. 4.1 - PROBLEM 4.16 Determine the maximum tension that...Ch. 4.1 - Two links AB and DE are connected by a bell crank...Ch. 4.1 - Prob. 4.18PCh. 4.1 - The bracket BCD is hinged at C and attached to a...Ch. 4.1 - The ladder AB, of length L and weight W, can be...Ch. 4.1 - The ladder AB, of length L and weight W, can be...Ch. 4.1 - A lever AB is hinged at C and attached to a...Ch. 4.1 - 4.23 and 4.24 For each of the plates and loadings...Ch. 4.1 - 4.23 and 4.24 For each of the plates and loadings...Ch. 4.1 - A rod AB, hinged at A and attached at B to cable...Ch. 4.1 - Fig. P4.25 and P4.26 4.26 A rod AB, hinged at A...Ch. 4.1 - For the frame and loading shown, determine the...Ch. 4.1 - Determine the reactions at A and C when (a) = 0,...Ch. 4.1 - Prob. 4.29PCh. 4.1 - Prob. 4.30PCh. 4.1 - Neglecting friction, determine the tension in...Ch. 4.1 - Fig. P4.31 and P4.32 4.32 Neglecting friction,...Ch. 4.1 - PROBLEM 4.33 A force P of magnitude 90 lb is...Ch. 4.1 - PROBLEM 4.34 Solve Problem 4,33 for a = 6 in,...Ch. 4.1 - Bar AC supports two 400-N loads as shown. Rollers...Ch. 4.1 - PROBLEM 4.36 A light bar AD is suspended from a...Ch. 4.1 - A 160-lb overhead garage door consists of a...Ch. 4.1 - Fig. P4.37 4.38 In Prob. 4.37, determine the...Ch. 4.1 - A movable bracket is held at rest by a cable...Ch. 4.1 - Fig. P4.39 4.40 Solve Prob. 4.39 when = 30.Ch. 4.1 - The semicircular rod ABCD is maintained in...Ch. 4.1 - Determine the range of values of for which the...Ch. 4.1 - The rig shown consists of a 1200-lb horizontal...Ch. 4.1 - Fig. P4.43 4.44 For the rig and crate of Prob....Ch. 4.1 - A 175-kg utility pole is used to support at C the...Ch. 4.1 - Knowing that the tension in wire BD is 1300 N,...Ch. 4.1 - Fig. P4.46 and P4.47 4.47 Determine the range of...Ch. 4.1 - Beam AD carries the two 40-lb loads shown. The...Ch. 4.1 - Fig. P4.48 and P4.49 4.49 For the beam and loading...Ch. 4.1 - A traffic-signal pole may be supported in the...Ch. 4.1 - A uniform rod AB with a length of l and weight of...Ch. 4.1 - Rod AD is acted upon by a vertical force P at end...Ch. 4.1 - A slender rod AB with a weigh of W is attached to...Ch. 4.1 - 4.54 and 4.55 A vertical load P is applied at end...Ch. 4.1 - 4.54 and 4.55 A vertical load P is applied at end...Ch. 4.1 - A collar B with a weight of W can move freely...Ch. 4.1 - A 400-lb weight is attached at A to the lever...Ch. 4.1 - A vertical load P is applied at end B of rod BC....Ch. 4.1 - Eight identical 500 750-mm rectangular plates,...Ch. 4.1 - A truss can be supported in the eight different...Ch. 4.2 - A 500-lb cylindrical tank, 8 ft in diameter, is to...Ch. 4.2 - Determine the reactions at A and E when =0.Ch. 4.2 - Determine (a) the value of for which the reaction...Ch. 4.2 - A 12-ft ladder, weighing 40 lb, leans against a...Ch. 4.2 - Determine the reactions at B and C when a = 30 mm.Ch. 4.2 - Determine the reactions at A and E. Fig. P4.66Ch. 4.2 - Determine the reactions at B and D when b = 60 mm....Ch. 4.2 - For the frame and loading shown, determine the...Ch. 4.2 - A 50-kg crate is attached to the trolley-beam...Ch. 4.2 - One end of rod AB rests in the corner A and the...Ch. 4.2 - For the boom and loading shown, determine (a) the...Ch. 4.2 - Prob. 4.72PCh. 4.2 - Determine the reactions at A and D when = 30.Ch. 4.2 - Determine the reactions at A and D when = 60.Ch. 4.2 - Rod AB is supported by a pin and bracket at A and...Ch. 4.2 - Solve Prob. 4.75, assuming that the 170-N force...Ch. 4.2 - The L-shaped member ACB is supported by a pin and...Ch. 4.2 - Using the method of Sec. 4.2B, solve Prob. 4.22....Ch. 4.2 - Knowing that = 30, determine the reaction (a) at...Ch. 4.2 - Prob. 4.80PCh. 4.2 - Determine the reactions at A and B when = 50....Ch. 4.2 - Determine the reactions at A and B when = 80.Ch. 4.2 - Rod AB is bent into the shape of an arc of circle...Ch. 4.2 - A slender rod of length L is attached to collars...Ch. 4.2 - Prob. 4.85PCh. 4.2 - A uniform plate girder weighing 6000 lb is held in...Ch. 4.2 - A slender rod BC with a length of L and weight W...Ch. 4.2 - A thin ring with a mass of 2 kg and radius r = 140...Ch. 4.2 - Prob. 4.89PCh. 4.2 - Prob. 4.90PCh. 4.3 - Two tape spools are attached to an axle supported...Ch. 4.3 - A 12-m pole supports a horizontal cable CD and is...Ch. 4.3 - A 20-kg cover for a roof opening is hinged at...Ch. 4.3 - END-OF-SECTION PROBLEMS 4.91 Two transmission...Ch. 4.3 - Solve Prob. 4.91, assuming that the pulley rotates...Ch. 4.3 - A small winch is used to raise a 120-lb load. Find...Ch. 4.3 - Two transmission belts pass over sheaves welded to...Ch. 4.3 - A 250 400-mm plate of mass 12 kg and a...Ch. 4.3 - Solve Prob. 4.95 for = 60. 4.95 A 250 400-mm...Ch. 4.3 - The rectangular plate shown weighs 60 lb and is...Ch. 4.3 - A load W is to be placed on the 60-lb plate of...Ch. 4.3 - An opening in a floor is covered by a 1 1.2-m...Ch. 4.3 - PROBLEM 4.100 Solve Problem 4.99, assuming that...Ch. 4.3 - PROBLEM 4.101 Two steel pipes AB and BC, each...Ch. 4.3 - PROBLEM 4.102 For the pipe assembly of Problem...Ch. 4.3 - PROBLEM 4.103 The 24-lb square plate shown is...Ch. 4.3 - PROBLEM 4.104 The table shown weighs 30 lb and has...Ch. 4.3 - PROBLEM 4.105 A 10-ft boom is acted upon by the...Ch. 4.3 - PROBLEM 4.106 The 6-m pole ABC is acted upon by a...Ch. 4.3 - PROBLEM 4.107 Solve Problem 4.106 for a = 1.5 m....Ch. 4.3 - A 3-m pole is supported by a ball-and-socket joint...Ch. 4.3 - PROBLEM 4.109 A 3-m pole is supported by a...Ch. 4.3 - PROBLEM 4.110 A 7-ft boom is held by a ball and...Ch. 4.3 - PROBLEM 4.111 A 48-in. boom is held by a...Ch. 4.3 - PROBLEM 4.112 Solve Problem 4.111, assuming that...Ch. 4.3 - PROBLEM 4.114 The bent rod ABEF is supported by...Ch. 4.3 - Prob. 4.114PCh. 4.3 - The horizontal platform ABCD weighs 60 lb and...Ch. 4.3 - PROBLEM 4.116 The lid of a roof scuttle weighs 75...Ch. 4.3 - PROBLEM 4.117 A 100-kg uniform rectangular plate...Ch. 4.3 - Solve Prob. 4.117, assuming that cable DCE is...Ch. 4.3 - PROBLEM 4.119 Solve Prob. 4.113, assuming that the...Ch. 4.3 - PROBLEM 4.120 Solve Prob. 4.115, assuming that the...Ch. 4.3 - PROBLEM 4.121 The assembly shown is used to...Ch. 4.3 - PROBLEM 4.122 The assembly shown is welded to...Ch. 4.3 - PROBLEM 4.123 The rigid L-shaped member ABC is...Ch. 4.3 - Prob. 4.124PCh. 4.3 - The rigid L-shaped member ABF is supported by a...Ch. 4.3 - Solve Prob. 4.125, assuming that the load at C has...Ch. 4.3 - Three rods are welded together to form a corner...Ch. 4.3 - Prob. 4.128PCh. 4.3 - Frame ABCD is supported by a ball-and-socket joint...Ch. 4.3 - Prob. 4.130PCh. 4.3 - Prob. 4.131PCh. 4.3 - PROBLEM 4.132 The uniform 10kg rod AB is supported...Ch. 4.3 - The frame ACD is supported by ball-and-socket...Ch. 4.3 - Solve Prob. 4.133, assuming that cable GBH is...Ch. 4.3 - The 8-ft rod AB and the 6-ft rod BC are hinged at...Ch. 4.3 - Prob. 4.136PCh. 4.3 - Prob. 4.137PCh. 4.3 - The pipe ACDE is supported by ball-and-socket...Ch. 4.3 - Solve Prob. 4.138, assuming that wire DF is...Ch. 4.3 - Two 2 4-ft plywood panels, each with a weight of...Ch. 4.3 - Solve Prob. 4.140, subject to the restriction that...Ch. 4 - A 3200-lb forklift truck is used to lift a 1700-lb...Ch. 4 - The lever BCD is hinged at C and attached to a...Ch. 4 - Determine the reactions at A and B when (a) h =0,...Ch. 4 - Neglecting friction and the radius of the pulley,...Ch. 4 - PROBLEM 4.146 Bar AD is attached at A and C to...Ch. 4 - PROBLEM 4.147 A slender rod AB, of weight W, is...Ch. 4 - PROBLEM 4.148 Determine the reactions at A and B...Ch. 4 - For the frame and loading shown, determine the...Ch. 4 - PROBLEM 4.150 A 200-mm lever and a 240-mm-diameter...Ch. 4 - The 45-lb square plate shown is supported by three...Ch. 4 - The rectangular plate shown weighs 75 lb and is...Ch. 4 - A force P is applied to a bent rod ABC, which may...
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