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- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/00%3A_Front_Matter/04%3A_PrefaceAnother drawback of MATLAB is that it is “proprietary”; that is, it belongs to MathWorks, and you can only use it with a license, which can be expensive. All programs in this book have been tested wit...Another drawback of MATLAB is that it is “proprietary”; that is, it belongs to MathWorks, and you can only use it with a license, which can be expensive. All programs in this book have been tested with Octave, so if you don’t have access to MATLAB, you should be able to work with Octave. Once you have Anaconda, you can install Octave by launching the Jupyter Prompt (on Windows) or a Terminal (on Mac OS or Linux), typing the following, and pressing enter:
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/09%3A_Ordinary_Differential_Equations/9.10%3A_ExerciseIf the temperature of the coffee drops by 0.7 °C during the first minute, how long will you have to wait to drink your coffee? You can answer this question with Newton’s Law of Cooling (see https://gr...If the temperature of the coffee drops by 0.7 °C during the first minute, how long will you have to wait to drink your coffee? You can answer this question with Newton’s Law of Cooling (see https://greenteapress.com/matlab/newton): dydt(t)=−k(y(t)−e) where y(t) is the temperature of the coffee at time t, e is the temperature of the environment, and k is a parameter that characterizes the rate of heat transfer from the coffee to the environment.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/02%3A_Scripts/2.03%3A_The_Fibonacci_SequenceThe Fibonacci sequence, denoted F, is a sequence of numbers where each number is the sum of the previous two. The following expression computes the nth Fibonacci number: \[F_n = \frac{1}{\sqrt...The Fibonacci sequence, denoted F, is a sequence of numbers where each number is the sum of the previous two. The following expression computes the nth Fibonacci number: Fn=1√5[(1+√52)n−(1−√52)n] In this example, the message says the error is in fibonacci, but the actual problem is that we have not assigned a value to n.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/15%3A_Under_the_Hood/15.04%3A_Chapter_ReviewIf you use these methods, and especially if you come to rely on them, you might find it unsatisfying to treat them as “black boxes.” At the risk of mixing metaphors, I hope you enjoyed opening the hoo...If you use these methods, and especially if you come to rely on them, you might find it unsatisfying to treat them as “black boxes.” At the risk of mixing metaphors, I hope you enjoyed opening the hood. I think the tools in this book are useful, and the ways of thinking are important, not just in engineering and science, but in practically every field of inquiry. Models are the tools we use to understand the world: if you build good models, you are more likely to get things right.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/13%3A_OptimizationThis chapter introduces fminsearch, which is a MATLAB function that searches for the maximum or minimum of a function.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/14%3A_Springs_and_Things/14.01%3A_Bungee_JumpingSuppose you want to set the world record for the highest “bungee dunk,” which is a stunt in which a bungee jumper dunks a cookie in a cup of tea at the lowest point of a jump. We can write Hooke’s Law...Suppose you want to set the world record for the highest “bungee dunk,” which is a stunt in which a bungee jumper dunks a cookie in a cup of tea at the lowest point of a jump. We can write Hooke’s Law as Fs=−kx where Fs is the force of the spring (bungee cord) on the jumper in newtons, x is the distance the spring is stretched in meters, and k is a spring constant that represents the strength of the spring in newtons per meter.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/15%3A_Under_the_HoodThis chapter reviews some of the MATLAB functions we’ve used—fzero, ode45, and fminsearch—and explains more about how they work.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/12%3A_Two_Dimensions/12.03%3A_ODEs_in_Two_DimensionsIf there is no wind and no spin on the ball, the ball travels in a vertical plane, so we can think of the system as two-dimensional, with x representing the horizontal distance traveled from the s...If there is no wind and no spin on the ball, the ball travels in a vertical plane, so we can think of the system as two-dimensional, with x representing the horizontal distance traveled from the starting place and y representing height or altitude. The goal of the rate function is to compute the derivative of W, so the output has to be a vector with four elements, where the first two represent the derivative of P and the last two represent the derivative of V.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/02%3A_Scripts/2.02%3A_Why_ScriptsLikewise, if you’re running a script repeatedly, it’s much faster to type the name of the script than to retype the code! But the great power of scripts comes with great responsibility: you have to ma...Likewise, if you’re running a script repeatedly, it’s much faster to type the name of the script than to retype the code! But the great power of scripts comes with great responsibility: you have to make sure that the code you are running is the code you think you are running. When you type the name of a script, MATLAB searches for the script in a search path, which is a sequence of folders. Be sure that the code you are running is the code you think you are running.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/11%3A_Second-order_systems/11.01%3A_Newtonian_Motionwhere F is the net force acting on an object, m is the mass of the object, and a is the acceleration of the object. So if we know acceleration as a function of time, how do we find the pos...where F is the net force acting on an object, m is the mass of the object, and a is the acceleration of the object. So if we know acceleration as a function of time, how do we find the position of the object, r? Well, we know that acceleration is the second derivative of position, so we can write the differential equation The first equation says that the first derivative of r is v; the second equation says that the first derivative of v is a.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Applied_Programming/Physical_Modeling_in_MATLAB_(Downey)/13%3A_Optimization/13.07%3A_ExercisesFor a given velocity, find the launch angle that maximizes the height of the ball when it reaches the wall. Write a simulation of the flight of a golf ball and use it to find the launch angle and allo...For a given velocity, find the launch angle that maximizes the height of the ball when it reaches the wall. Write a simulation of the flight of a golf ball and use it to find the launch angle and allocation of spin and initial velocity (for a fixed energy budget) that maximizes the horizontal range of the ball in the air. The lift of a spinning ball is due to the Magnus force (see https://greenteapress.com/matlab/magnus), which is perpendicular to the axis of spin and the path of flight.
