...Sailboat Stability MAT222 Ms. Scarf July 29, 2014 Sailboat Stability This weeks assignment is found on page 605 of our math book, question number 103. Focus is solving formulas and using a vocabulary that describes the steps in the equations in mathmatical terms. This weeks focus is radical equations/formulas. The specific problem assigned gives real world value in understanding sailboats and the mathematical understanding of when the stability could be compromised or ideal. The problem is as follows: Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2. For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. C=4d-1/3 b (Dugopolski,2012) There are three parts to this problem a, b, and c. Each one will be worked out. a)Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam 13.5ft. Using the formula and substituting the values given for the variables of d and b: C=4(23245)-1/3(13.5) First work the exponent by using the reciprocal due to the negative value C=4(.035)(13.5) Multiply all C=1.89 This is the capsize screening value(notice it is below 2 as needed) b) Solve for d of the formula C=4d-1/3b Start isolating d by dividing both sides by 4b C/4b=d-1/3 Now resolve...
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...BUSI 2701 D Assignment # 1 – Business Report - Country Analysis You are an executive working at a large Canadian company that is considering expanding its foreign operations. The CEO has asked you to do an analysis of one of the target countries and provide a recommendation as to whether or not to proceed. Please note that you are being asked to do a general analysis of the country. You are not doing the analysis based on any one company or industry. The CEO is a very busy person so it is important that the report be written in a clear and concise manner. It will be judged on the factual information it contains, the clarity of your argument and the depth of your analysis. Please note that you should not try to gather data that supports only one side or the other of whether or not to proceed. Rather, you should gather all the pertinent data and let your analysis guide you to the best recommendation. The report is to be submitted via CU Learn, due on the date indicated in the course outline. The paper is to be a maximum of seven (7) pages (doubled spaced, 12 pt font, 2.54 cm margins) plus title page, references, endnotes, and appendices if any. If the report is longer than seven pages, only the first seven pages will be read and graded. The title page must contain your name, student number and the country you have chosen from the list provided. The first half page (maximum) of the report will be an executive summary of the report’s highlights and your recommendation...
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...taking the company to another level? In order for this hypothesis to work, Books R Us needs to start planning for the future. The hypothesis is taking a look at the larger scale book stores. Finding the correct marketing tool is imperative to the increase and fluidity of sales for Books R Us. According to Doug Gottieb, Barnes and Noble’s creative director, they have increased sales on eBooks, physical books, music and DVD’s because of new free phone application that individuals have downloaded onto their phones. This information is again crucial to the growth of BRUS. These variables are not part of the data that support the information provided. The fluctuation in sales from week to week, explain that the BRUS needs more financial stability. What would happen to BRUS if they execute new innovative ideas that could bring revenue and sales to the company? Has Books R US taken the opportunity to hire a creative director that can implement new ideas regarding technology? What kinds of surveys have been conducted to illustrate improvements for the company? These are several questions that go unanswered for lack of research. So my hypothesis is if Books R Us can answer these questions and create new ideas that will be beneficial to the success of the company; then the fluctuation in sales will be limited and they will continue to stabilize and increase instead of decrease. Staying marketable increases sales and profitability; this goes with any business venture. Book R Us needs...
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...task difficulty and effort. These four categories can be split into 2 sub-groups Internal/ external and stable/unstable. 2. Attribution theory looks at the reason for why someone failure or succeeded in a certain situation. This is important from a sports psychologists view because models such a Wieners give people the ability to blame their failure on external reasons out of there control and therefore keep motivation high. 3. The locus of causality dimension indicates whether the attribution relates to factors that are either internal or external to the performer. Effort and ability represent internal factors while task difficulty and luck are external and are known as environmental variables. Stability indicates whether attributions are stable or unstable. Stability refers to the degree of permanence associated with an attribution factor. A stable factor is considered permanent and unchangeable, for example ability. An unstable factor, by contrast, is temporary and can be changed. Luck is an example of an unstable factor. Control, which will be considered later, is a third dimension of the attribution model. It is not referred to directly in the specification but is a key factor in the important process of attribution retraining. 4. If a hockey player continues to lose because the teams are playing are constantly better then he or she will start to become depressed or try to avoid the sport in general because he or she does not think there is a point of playing...
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...1914, the stability of Russia was questionable to say the least. Historians continually argue about what factors mean that Russia was stable or unstable. Some evidence is clear for example the Tsar still being in control of his ministers and other evidence is arguable, for example the increase in population, this could be indicating a prosperous time in Russia and an increase in stability, or it could mean there was a lack of activities to be done, and the increased population meant there were more mouths to feed. There are many factors that contribute to how stable Russia was at this time. Economically, Russia seemed more unstable: eighty percent of the population were peasant farmers and the gap between the rich and poor was only increasing, making Russia even more unstable than it already was. Autocracy continued to repress the poor and the rich continued to hold most of the country’s finances. The poor struggled to become economically active, the rich fought to keep things the way they were during this time period. Stolypin tried to help the peasants by introducing land reforms – these meant that peasant’s owned the land and had more of an incentive to maintain and produce from it. However Stolypin was not supported in this and a lot of the peasants believed in the commune, they didn’t want privatisation for social and economic reasons. There was a massive pressure on the land and due to the fact that there was no unrest at this time indicates that the stability had increased...
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... Links to Good Landslide and Slope Failure sites: | USGS Landslide News and Information - http://landslides.usgs.gov/html_files/landslides/hawaii99.html | | http://walrus.wr.usgs.gov/elnino/landslides-sfbay/photos.html contains a computer-simulated landslide | | Landslides at Hagerman Fossil Beds, Idaho - http://www.nps.gov/hafo/landslides.htm | | Yosemite landslide News - http://landslides.usgs.gov/html_files/landslides/Yosemite99.html | SLOPES Material is constantly moving downslope in response to gravity. Movement can be very, very slow, barely perceptible over many years. . . . . Or, movement can be devastatingly rapid, apparent within minutes. Whether or not slope movement occurs depends on slope steepness and slope stability. Slope Profile Some slopes are gently rounded, while others are extremely steep. Profiles of naturally-eroded slopes are primarily dependent on climate and rock type. Resistant rock and rock from semi-arid regions have similar profiles because in both cases chemical...
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...(z) + y(−1)z) + z −2 (Y + (z) + y(−1)z + y(−2)z 2 ) = (2 + 3z −1 +z −2 )Y + (z) + [(3y(−1) + y(−2)) + z −1 y(−1)] = (1 + z −1 − z −2 )U (z) 1 + z −1 − z −2 (3y(−1) + y(−2)) + z −1 y(−1) Solve: Y (z) = U (z) − 2 + 3z −1 + z −2 2 + 3z −1 + z −2 + zero−state response zero−input response 1 1−z −1 ; Plug in: u(n)=unit step→ U (z) = U + (z) = Y + (z) = Partial: fraction 1+z −1 −z −2 (2+3z −1 +z −2 )(1−z −1 ) 4/3 1+ 1 z −1 2 y(−1) = 2, y(−2) = −1: = −4+4z −1 +z −2 2(1+ 1 z −1 )(1+z −1 )(1−z −1 ) 2 − 5+2z −1 2+3z −1 +z −2 Y + (z) = − 7/2 1+z −1 + 1/6 . 1−z −1 Note no constant term. Z −1 : y(n) = 7 4 1 n 1 (− ) u(n) − (−1)n u(n) + u(n). 3 2 2 6 natural response forced EECS 451 ZERO-INPUT RESPONSE AND STABILITY Given: 2y(n) + 3y(n − 1) + y(n − 2) = u(n) + u(n − 1) − u(n − 2) (previous) [3y(−1) + y(−2)] + z −1 y(−1) 1 + z −1 − z −2 U (z) − Soln: Y...
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...These site www.tulane .edu/~sanelson/Natural_Disasters/masswastproc.htm provides in-depth information about mass movements and the processes involved in the movement. It gives quite a number of causes of the earth movement and mostly how the human activities impact the processes. As human population increase and occupy more space on the earth surface, the mass movement processes have become more likely to have effect on human beings. The site also provides a tally in a table showing the mass movement impact on the human life over the past century. The website reveals that landslides in United States have caused roughly more than $2b in damages and (25-50) deaths. It clearly cuts to edge that the less developed countries have the highest number of losses because of population being high, lack of laws of zoning, lack of data regarding mass movement hazards and lack of preparedness on emergency issues. In addition the website cites that knowledge concerning geology and movements of mass can result to a better arrangement that can decrease vulnerability to such kind of hazards. The website further looks at the types or rather categories of mass movement process. They are divided into two broad types, sedimental flow and slope failure and then further into subcategories. Mass movement process in cold climates is also featured in the site. The information provided in the site corresponds to the reading based on mass wasting and mass wasting processes and can be helpful in my daily...
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...STUDY OF SLOPE STABILITY IN LIGNITE MINES By Mamta Jaswal (090610122047) Nilay J. Patel (090610122029) Ashish D. Patel (090610122026) Satish B. Patel (090610122013) Supervised by: Prof. Rajesh Arora M. Tech. A project part-1 submitted to Gujarat Technological University In partial fulfilment of The Requirements for the Degree of Bachelor of Engineering In Mining Engineering October 2012 CERTIFICATE This is to certify that Ms. Mamta Jaswal of BE. Semester VII (Mining engineering) has completed her one full semester on project work Titled “STUDY OF SLOPE STABILITY IN LIGNITE MINES” Satisfactorily in partial fulfilment of requirement of Bachelor of Engineering In Mining Engineering, Gujarat Technology University, Ahmedabad in the year 2012. Date: / / 2012 Place: Palanpur Internal Guide Prof. V.J. Sharma Prof. Rajesh Arora Head of Department (Mining engineering) Seal of institute CERTIFICATE This is to certify that Mr. Nilay J. Patel of BE. Semester VII (Mining engineering) has completed his one full semester on project work Titled “STUDY OF SLOPE STABILITY IN LIGNITE MINES” Satisfactorily in...
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...Surya Hope) is in process to save the survivors of the disaster. The Indian Air Force, Army, ITBP personnel are engaged day and night to help the people struck in the Himalayan state. Whereas, when seen from the perspective of geologists, if stricter regulations would have existed then the losses from the destructions would have been lesser. Every section of the society is having a different story to say following their scientific knowledge, belief in God and nature and many more things. Few are blaming the central and the state government for turning their blind eye, towards plundering the hills. The heavy rainfall created havoc by affecting the fragile nature of the Himalayan range that is known for its poor soil stability in its steep slopes. Apart from the stability of soil in the peaks of the youngest mountains of the world, the other reasons for the disaster as per the expert are: the blind expansion of the hydro-power projects and...
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...A Case Study in Approximate Linearization: The Acrobot Example Richard M. Murray Electronics Research Laboratory University of California Berkeley, CA 94720 John Hauser Department of EE-Systems University of Southern California Los Angeles, CA 90089–0781 Memorandum No. UCB/ERL M91/46 29 April 1991 Electronics Research Laboratory College of Engineering University of California, Berkeley 94720 A Case Study in Approximate Linearization: The Acrobot Example Richard M. Murray∗ Electronics Research Laboratory University of California Berkeley, CA 94720 murray@united.berkeley.edu John Hauser† Department of EE-Systems University of Southern California Los Angeles, CA 90089–0781 hauser@nyquist.usc.edu 29 April 1991 Abstract The acrobot is a simple mechanical system patterned after a gymnast performing on a single parallel bar. By swinging her legs, a gymnast is able to bring herself into an inverted position with her center of mass above the part and is able to perform manuevers about this configuration. This report studies the use of nonlinear control techniques for designing a controller to operate in a neighborhood of the manifold of inverted equilibrium points. The techniques described here are of particular interest because the dynamic model of the acrobot violates many of the necessary conditions required to apply current methods in linear and nonlinear control theory. The approach used in this report is to approximate the system in such a way that the behavior...
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...Rotational Slumping A slump is a form of mass wasting that occurs when a large mass of loosely materials or rock layers moves a short distance down a slope. Movement is characterized by sliding along a curved surface. Causes of slumping include earthquake shocks, thorough wetting, freezing and thawing, undercutting, and loading of a slope. Rotational slumps occur when a slump block, composed of sediment or rock, slides along a concave-upward slip surface with rotation about an axis parallel to the slope. Rotational movement causes the original surface of the block to become less steep, and the top of the slump is rotated backward. This results in internal deformation of the moving mass consisting chiefly of overturned folds called sheath folds. Slumps have several characteristic features. The cut, which forms as the landmass breaks away from the slope, is called the scarp and is often cliff-like and concave. In rotational slumps, the main slump block often breaks into a series of secondary slumps and associated scarps to form stair step pattern of displaced blocks. The upper surfaces of the blocks are rotated backwards, forming depressions that may accumulate water to create ponds or swampy areas. The surface of the detached mass often remains relatively undisturbed, especially at the top. However, hummocky ridges may form near the toe of the slump. Addition of water and loss of sediment cohesion at the toe may transform slumping material into an earthflow. Thorough wetting...
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...where µ(x) is a mass matrix, τ is an inertia matrix, F (x, x, x) is a vector of generalized ˙ ¨ resultant forces, x0 = (x1,0 , x2,0 ....xn,0 ) is a reference configuration and K is a matrix of joint stiffnesses. Select state variables for the system and write down the state equations. Under what conditions is the system linear? Proof. Assuming a two-link system: Let y1 = x1 , y2 = x1 , y3 = x1,0 , y4 = x1,0 be the state ˙ ˙ variables of the manipulator. Then, y 1 = x1 y2 = −µ−1 (x1 )[F (x1 , x1,0 ) + K(x1 − x1,0 )] y3 = x1,0 y4 = τ −1 K(x1 − x1,0 ) + τ −1 u where u is the input vector. 1 Problem 2. Analyze the following equations graphically. In each case sketch the vector on the phase plane, find all the fixed points, classify their stability, and sketch the graph for different initial conditions.Attempt to obtain the analytical solution for x(t). • x = − sin(x) ˙ • x = x − x3 ˙ • x = e−x sin(x) ˙ Proof. .... 1. x = − sin(x) ˙ 1 sin x sin x − sin x = − sin x2 = − 1−cos x2 ⇒ Let u = cos x ⇒ du = − sin xdx ⇒ du 1−u2 → −0.5 ln |u − 1| + 0.5 ln |u + 1| Analytical Solution is ⇒ t = −0.5 ln | cos x − 1| + 0.5 ln | cos x + 1| Fixed points for this differential equation are the points where x = 0 are at x0 = nπ. ˙ Intuitively, when n = even, the solution is ‘stable’. When n=odd, the pendulum is inverted, and hence ‘unstable’. 2 2. x = x − x3 ˙ 1 x−x3 1 ⇒ (x + x ) 1−x2 = 1 x(1−x2 ) = 1 x + x 1−x2 = ln |x| + 0.5 ln |1 − x| − 0.5 ln |1 + x| ...
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...output as yaw rate. Plot the step response for a steering angle input. cF cR m .v CoG CoG c l c l F F R R JZ cR lR cF lF cF 1 2 m .v mCoG .vCoG CoG CoG W 2 2 c R l R c F l F c F l F JZ J Z .vCoG y 0 1 Also determine the stability limits for the open loop transfer function via root locus. The vehicle parameters are as follows: mCoG = 1450 kg; vCoG = 15 m/s; lF = 1.05 m; lR = 1.5 m; JZ = 2545 kg-m2; cF = 25500 N/rad; cR = 62000 N/rad; Iwi = 1.1 kg-m2; reff = 0.3 m; 2. For the vehicle parameters stated in problem 1, design a steering-based (control input being w) yaw stability control system with proportional-integral-derivative (PID) terms to obtain a desired natural frequency of 9 rad/sec and damping ratio of 0.5. Also, assume that the vehicle is 1.5 m wide and center of gravity is located at the center. Determine the closed loop system response for step and ramp inputs. What are your PI gain values? Note your observations on the stability of the closed loop system. 3. Given the vehicle parameters in problem 1, design a PI (proportional plus integral) anti-lock brake control system for the vehicle to maintain a desired slip ratio of 0.15. Assume that the desired damping ratio of 0.6 and desired natural frequency is 10 Hz for...
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...agent system to assist a vehicles operator the features and vehicles employing them are labeled as smart or intelligent vehicles. They are used for automation of difficult tasks, especially navigation, may be referred to as the semi-autonomous. a vehicle solely relying on automation is known as autonomous . After the invention of the integrated circuit, the sophistication of the automation technology has increased. Manufacturers and researchers have subsequently added a variety of automated functions to automobiles and other vehicles There may be many ways of vehicular automation, but some of the important ones are as follow: * Cruise control * ABS (Antilock Breaking System) * Traction control system * Electronic Stability Control * Hill Descent Control System (HDC) CRUISE CONTROL Cruise control (sometimes known as speed control or autocruise, or tempomat in some countries) is a system that automatically controls the speed of a motor vehicle. The system is a servomechanism that takes over the throttle of the car to maintain a steady speed as set by the driver. HISTORY Speed control with a centrifugal governor was used in automobiles as early as 1900 in the Wilson-Pilcher and also in the 1910s by Peerless. Peerless advertised that their system would "maintain speed whether up hill or down". The technology was adopted by James Watt and Matthew Boulton in 1788 to control steam engines...
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