...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| The analytical...
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...of works?” God and Adam entered into a covenant in which if Adam did not sin, he would be removed from probationary period and reciveve a confirmed state of immortality. What opinion does the textbook purpose regarding the nature of the Tree of Life’s existence? It was instrument to test the motives of Adam, to reveal if he could demonstrate his virture through obedience Know the three avenues of temptation through which Satan tempted Eve. 1.Lust of the eyes 2.Lust of the flesh 3.Pride of life Understand the distinctions between the Arminian and Calvinist views of total depravity, and be able to provide a biblical definition of it. Arminian: Man can reason himself to God fully developed in the enlightment era. Man is capable of doing spiritual good. Moral works can be performed. Calvinism: Man cannot reason except trhough the grace of God. Man can do not good until salvation occurs. No moral works can be performed. Biblical Definition: Man can reason, but he can’t obtain merit from God. Man is unable to do spiritual works unless he is regenerated. Socially moral works can be performed by unbelievers What is the textbook’s view regarding the nature (or reality) of the serpent found in Genesis 3? Satan used an actual serpent. At what point (and through what event) was the promise of God to “crush” Satan’s head fulfilled? At Calvary when Satan was judged Understand the nature of sin as revealed by Old Testament words as well as by New Testament...
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...the textbook reach regarding the legitimacy of a “covenant of works?” God and Adam entered into a covenant in which if Adam did not sin, he would be removed from a probationary period and receive a confirmed state of immortality. • What opinion does the textbook propose regarding the nature of the Tree of Life’s existence? It was an instrument to test the motives of Adam, to reveal if he could demonstrate his virtue through obedience. • Know the 3 avenues of temptation through which Satan tempted Eve. 1. Lust of the eyes. 2. Lust of the flesh. 3. Pride of life. • Understand the distinctions between the Arminian and Calvinist views of total depravity, and be able to provide a biblical definition of it. Man cannot reason except through the grace of God. Man can do know good until salvation occurs. No moral works can be performed. Man can reason, but he can't obtain merit from God. Man is unable to do spiritual works unless he is regenerated. Socially moral works can be performed by unbelievers. • What is the textbook’s view regarding the nature (or reality) of the serpent found in Genesis 3? Satan used an actual serpent. • At what point (and through what event) was the promise of God to “crush” Satan’s head fulfilled? At Calvary when Satan was judged. • Understand the nature of sin as revealed by Old Testament and New Testament words. Note the emphasis upon outward acts in Old Testament words and upon inward disposition...
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...philosophical and theological thinking. He gives accounts of his faults to God genuinely and praises God with authenticity, along which he takes the chance to think about the origin of sins. In Book I, he narrates his observation on a little baby to explain that even very young children have the tendency of being selfish, when “he could not yet speak and, pale with jealousy and bitterness, glared at his brother sharing his mother’s milk.” It seems that the tendency towards self over others is rooted within our instinct. However, the selfishness during childhood is unthinking and is usually tolerated by people because “with coming of age it will pass away.” That is, when human enter early adolescence, they gradually gain the ability to understand what’s right or wrong and to ponder sin like adults do. While, it’s quite interesting that Augustine uses his story of stealing pears with peers to illustrate the fact that even if when human beings have clear knowledge of wrongdoing, they may still have those sinful behaviors possibly for some satisfactions. He states in Confessions: “wickedness filled me,” and “my desire was to enjoy not what I sought by stealing but merely the excitement of thieving and the doing of what was wrong.” (Book II) This thought by Augustine indicates that not only sin is rooted in our nature, but also the impulse of desiring for wickedness hides underneath. Though with the constraint by ethics, it may still be somewhat hard for people to...
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...as it sounds. It is how Christians view the world around us. Although, the real definition for it is a particular philosophy of life or conception of the world. The question of origin is “where did we come from”. The answer to that is God created Adam then created Eve from Adam to produce life. There are many verses in the Bible on origin however I can only give two examples. My first example is 2 Chronicles 24:13 the second verse to go along with origin would be of course Genesis 2:4-25. The next would be the question of identity. The Bible answers the question “what does it mean to be human” by stating that men were created in God’s image. The two verses that support that would be Genesis 1:26-28 and Psalms 8:5. The meaning is “why do I exist”. The purpose of life is to walk and dwell amongst the Lord our God. The two verses I chose to go with this are 2 Corinthians 1:4 and Romans 15:13. The question of Morality is doing what god wants us to do and using the Bible as our sword. Its about living for god. Genesis 3 and Exodus 20:6 are the verses I chose to go with morality. The question of destiny “is there life after death, where will I go when I die”. We as Christians believe that if we follow God and serve him without sin we will go to Heaven but if we chose not to follow him and to commit sins we will go to Hell where there you will spend eternity without...
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...that God is made up of three persons- the Holy Trinity- and that Jesus is the Son of God and savior of humanity while Islam believe Allah is only one God and He is the creator of all things and has no offspring, race or gender. All in all, these two religions, though having a similar origin, have different views on Jesus Christ, teachings, and scriptures. Islam was founded by a prophet named Mohammed in the approximate year of 610. At the age of forty, he was supposedly visited by the Angel Gabriel, who presumably told him the fundamentals of Islam, while in a cave near Mecca, a city in Saudi Arabia.1 Corinthians 15: 1-4 states that Jesus Christ preached the gospel and we are saved by it. It was he who sent out apostles to spread God's word throughout the world, it was he who died for the world; and it was he who founded Christianity. Jesus Christ, the Son of God, and Mohammed, a prophet...
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...would appear, there are so many other factors that combine to make up an individuals worldview. Some of these factors include, the persons origin, where they are from, what belief system that they adhere to. The education they were given, what type of things that they were taught as they were growing up, which comes down to what others around that person hold to be true and have possibly become an influence their own perceptions. Essentially a worldview is the perception of the world, that an individual comes to based on that persons ideas and the beliefs that they hold to be true. According to Weider and Gutierrez (Consider, 2011) a worldview can also be described as the framework that a person uses in decision making, a filter or a lens that a person may use to interpret their life and the world around them, and basically a persons philosophy of life. (Consider, p. 51) One of the bigger aspects that people use when attempting to interpret their lives and the world that they live in is a religious or biblical aspect. As Christians our beliefs influence our worldviews, the lens that we see through significantly differs from what others may conclude when it comes to topics such as how we believe man came into existence, the origin of man, as well as meaning and purpose, identity, morality, and destiny. The question of the origin of man and how he came into existence is much debated. Scientist would have you believe that we started out as matter and through the process...
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...WORLD RELIGIONS – REL 212 World Religions HINDUISM & JAINISM WEEK 2 Cosmogony Origin of the Universe Hinduism and Jainism cosmogony origin of the universe is that there isn’t no specific origin or founder. Nature of God/Creator The Gods are in male and female form and represent many different things. View of Human Nature Hinduism and Jainism: Karma is what comes around goes around. View of Good & Evil Hinduism and Jainism: Good actions have a good effect and bad actions have a bad effect. “Karma”. View of Salvation Hinduism and Jainism salvation is called Moksha. It’s when an enlightened human being is freed from the cycle of lifeanddeath and comes into a state of completeness. And the Jainism salvation is achieved through three cycles right belief, right knowledge, and right conduct. Hinduism and Jainism: Samsara reincarnation is taught that the soul leaves the dead body and enters a new body. They believe in the rebirth and reincarnation of the souls. Jainism following liberation one’s jiva ascends to the apex of the universe to join the other siddhas. One can ascend to a heavenly realm due too good karmas accrued but must return to a human incarnation in order to achieve final liberation. Hinduism and Jainism: Practices (both): Praising the Cow called “The Cow is our Mother, for she gives us her milk.” Worship with fire, yoga, sacred chants, verbal formulas, and sacred actions. Worship deity images, pictures and sculptures...
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...In The Lost World of Adam and Eve, Walton presents Genesis 1-3 in a way that many have never thought of before. Walton uses his extensive study of Ancient Near East texts and an open minded interpretation of Genesis in order to develop his theories. Walton proposes that the Genesis account is not a material origin but a functional origin Walton raises 21 “propositions” to present his case. Walton’s opening proposition brings to light that modern readers of Genesis are in a very low context setting of communication. This means that because we are separated by a large period of time, language, and cultural difference, we are not viewing the author’s words within the context they were originally given; therefore, it is very likely that we are...
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...through the function text. Target face and probabilities a) What is the probability of hitting any possible point within the inscribed area of radius ½? To draw the inscribed circle, apply a shrinking factor to both sin(a) and cos(a) in polygon function: > polygon(.5*sin(a),.5*cos(a),col="red") Dart game – CompTools2012 user guide In this user guide we are going to solve some problems related to the dart game. Follow us step by step and enjoy the game! We want to build a target face for throwing darts, like the one in the figure. We assume that it is a circle of radius 1 with center in the origin point. For the construction of the target, the reference is paragraph 6.2 of Using R for scientific computing by Karline Soetaert. We present here the necessary script: > a plot(cos(a),sin(a),type="l",lwd=2,xlab="" ,ylab="",axes=T, asp=1) Ten Inner circles at equal distance: > for (i in seq( 0.1,0.9,by=0.1)) lines(i*sin(a), i*cos(a)) >polygon(sin(a)*0.1,cos(a)*0.1,col="red") > for (i in 1:10) text(x = 0, y = i/100.025, labels = 11-i, font = 2) >for (i in 1:9) text(x = 0, y = -1 + (i/10-0.025), labels = i, font = 2) The polygon command will cover the inner circles: launch again the previous for loops to obtain the following image: > for (i in seq( 0.1,0.9,by=0.1)) lines(i*sin(a), i*cos(a)) > for (i in 1:10) text(x = 0, y = i/100.025, labels = 11-i, font = 2) >for (i in 1:9) text(x = 0, y = -1 + (i/10-0.025), labels = i, font = 2) 1 Croce...
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...the polar form Introduction 10.2 In this Block we introduce a geometrical interpretation of a complex number. Since a complex number z = x + iy is comprised of two real numbers it is natural to consider a plane in which to place a complex number. We shall see that there is a close connection between complex numbers and two-dimensional vectors. In the second part of this Block we introduce an alternative form, called the polar form, for representing complex numbers. We shall see that the polar form is particularly advantageous when multiplying and dividing complex numbers. 9 6 x know what a complex number is Prerequisites Before starting this Block you should . . . 8 y understand how to use trigonometric functions cos θ, sin θ and tan θ z understand what a polynomial function is { possess a knowledge of vectors 7 Learning Outcomes Learning Style After completing this Block you should be able To achieve what is expected of you . . . to . . . represent complex numbers on an Argand diagram obtain the polar form of a complex number multiply and divide complex numbers in polar form allocate sufficient study time briefly revise the prerequisite material attempt every guided exercise and most of the other exercises 1. The Argand diagram In Block 10.1 we met a complex number z = x + iy in which x, y are real numbers and √ i = −1. We learned how to combine complex numbers together using the usual operations of addition, subtraction, multiplication and division...
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...VECTOR FUNCTIONS VECTOR FUNCTIONS Motion in Space: Velocity and Acceleration In this section, we will learn about: The motion of an object using tangent and normal vectors. MOTION IN SPACE: VELOCITY AND ACCELERATION Here, we show how the ideas of tangent and normal vectors and curvature can be used in physics to study: The motion of an object, including its velocity and acceleration, along a space curve. VELOCITY AND ACCELERATION In particular, we follow in the footsteps of Newton by using these methods to derive Kepler’s First Law of planetary motion. VELOCITY Suppose a particle moves through space so that its position vector at time t is r(t). VELOCITY Vector 1 Notice from the figure that, for small values of h, the vector r(t h) r(t ) h approximates the direction of the particle moving along the curve r(t). VELOCITY Its magnitude measures the size of the displacement vector per unit time. VELOCITY The vector 1 gives the average velocity over a time interval of length h. VELOCITY VECTOR Equation 2 Its limit is the velocity vector v(t) at time t : r(t h) r(t ) v(t ) lim h 0 h r '(t ) VELOCITY VECTOR Thus, the velocity vector is also the tangent vector and points in the direction of the tangent line. SPEED The speed of the particle at time t is the magnitude of the velocity vector, that is, |v(t)|. SPEED This is appropriate because, from Equation 2 ...
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...“Someone with a biblical worldview believes his primary reason for existence is to love and serve God.” Part II 1. When we think about origin through the Christian worldview, the first “tool” we should think about is. The bible is the first “stepping stone” for the Christian worldview; it’s what we use to base our beliefs on, and how we know that God is the almighty creator. Genesis 1:24 and Genesis 2:7 are good supporting scripture references that talk about how God is the creator, thus the origin of Christian worldview is formed. 2. The bible says that God created man and women in his image and that we are a “unique creation.” Knowing that God only created US in him image and nothing else helps us answer the questions of identity. Genesis 1:27 and 1 Corinthians 6:19-20 are scripture references that further reiterate that man was formed in God’s image and we should be respectful of ourselves because “our body is a temple of the Holy Spirit.” 3. In my opinion the purpose of life as far as biblical worldview is concerned is so that man will come to know and accept Jesus Chris as their Lord and Savior. 2 Corinthians 5:15 let’s us know that Jesus died for us, and paid for our sins. He did this so that we may live to Glorify him. Jeremiah 29:11 is another good scripture reference to further develop the concept of the Purpose origin. 4. We as Christians use the Bible as our “guide to life.” It’s what we use to determine what is right or wrong and how we should live...
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...according to the Gregorian calendar, and is observed by fasting and having day-long religious services. The meaning of this day is to atone for one’s sins with God, and to demonstrate repentance and make amends. Yom Kippur is the most important day of the year for people of Jewish faith. Origin of Yom Kippur According to author Amy J. Kramer (2010), “The first Yom Kippur took place after Moses returned from his second trip to Mt. Sinai with the replacement set of tablets containing the Ten Commandments” (para. 2). Moses broke the original tablets containing the Ten Commandments when he returned from Mount Sinai the first time to find the Jewish people worshipping a golden calf, instead of God. He returned to Mount Sinai for the second time on the first day of the Jewish month of Tishri. The Jewish people, who were truly repentant for what they had done, fasted the entire time the sun was up. Moses returned from Mount Sinai on the tenth day of the month of Tishri, and found that the Jewish people were honestly sorry for the sins they had committed. He declared that the tenth day of Tishri would be a day of atonement for all generations of Jews to come. The month of Tishri is usually either September or October when using the secular calendar, and the actual day Yom Kippur falls on varies from year to year. This is the origin of the Yom Kippur holy day. General Religious Practices on Yom Kippur On Yom Kippur,...
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...The consequences of sin were devastating, not only for Adam and Eve but also for the entire human race. The sad story of human history is replete with numerous examples of sin’s repercussions: wars, genocide, human sex trafficking, slavery, racism, and injustice to name just a few. Different philosophies and worldviews attempt to explain the presence of evil in the world with some, despite the evidence, even denying evil exists. Only the Christian worldview adequately explains such iniquity: sin. Although the Bible does not reveal the origin of sin (Zuck, 1991, p. 18), the first twelve chapters Genesis not only describe the entrance of sin into the world and trace its development, they also hint at the nature of sin, its consequences, and the solution to sin. The Progression of Sin The consequence of sin, death, manifests itself the moment Adam and Eve eat the fruit from the tree of knowledge of good and evil. Bartholomew and Goheen (2009) recognize that on the surface, Adam and Eve do not immediately die. Or do they? The physical life of Adam and Eve does not stop in the instant they taste the fruit: this isn’t the poison apple of the fairy tale. But something deep inside them and between them does die. Their sense of themselves and their...
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