Engineering: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=164
en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 01 Oct 2020 16:48:45 GMTThu, 01 Oct 2020 16:48:45 GMTNew applications in the Engineering categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgEngineering: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=164
Minimal Road Radius - From a physics educator's perspective
https://www.maplesoft.com/applications/view.aspx?SID=154648&ref=Feed
This problem solves for the minimal radius of curvature for designing and building a banked curve on a road assuming a constant speed and elevation.
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It is written using the modern mechanics introductory physics approach of Chabay and Sherwood and demonstrates the pedagogical value of Maple's ability to teach physics and to solve problems starting from fundamental principles, i.e., a top-down approach. This is in contrast to most computational systems where one codes starting from a specific example before implementing the fundamental principles.<img src="https://www.maplesoft.com/view.aspx?si=154648/Banked_Curve_Image.jpg" alt="Minimal Road Radius - From a physics educator's perspective" style="max-width: 25%;" align="left"/>This problem solves for the minimal radius of curvature for designing and building a banked curve on a road assuming a constant speed and elevation.
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It is written using the modern mechanics introductory physics approach of Chabay and Sherwood and demonstrates the pedagogical value of Maple's ability to teach physics and to solve problems starting from fundamental principles, i.e., a top-down approach. This is in contrast to most computational systems where one codes starting from a specific example before implementing the fundamental principles.https://www.maplesoft.com/applications/view.aspx?SID=154648&ref=FeedMon, 15 Jun 2020 04:00:00 ZProf. Scot GouldProf. Scot GouldBraking Distance of a Skidding Car
https://www.maplesoft.com/applications/view.aspx?SID=154632&ref=Feed
You're driving a car on an incline, but the brakes lock up. How far will your car skid?
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This application uses Newton's 2nd law and laws of motion to derive an equation that gives the distance your car will skid (also known as the braking distance). This equation shows that the braking distance is proportional to the square of the velocity at the start of the skid.<img src="https://www.maplesoft.com/view.aspx?si=154632/Braking_Distance_of_a_Skidding_Car.png" alt="Braking Distance of a Skidding Car" style="max-width: 25%;" align="left"/>You're driving a car on an incline, but the brakes lock up. How far will your car skid?
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This application uses Newton's 2nd law and laws of motion to derive an equation that gives the distance your car will skid (also known as the braking distance). This equation shows that the braking distance is proportional to the square of the velocity at the start of the skid.https://www.maplesoft.com/applications/view.aspx?SID=154632&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanFirst equilibrium condition
https://www.maplesoft.com/applications/view.aspx?SID=154624&ref=Feed
With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154624/first_eq.png" alt="First equilibrium condition" style="max-width: 25%;" align="left"/>With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154624&ref=FeedWed, 01 Apr 2020 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloAtwood Machine
https://www.maplesoft.com/applications/view.aspx?SID=154598&ref=Feed
The following is a detailed study of the motion of an unconventional Atwood Machine where one mass is constrained to move along a fixed vertical axis.
The differences with the regular Atwood Machine are :
1- the tension T on the string on either side of the pulley though it is the same, however it is not constant in the present case because of the obliquity of the 2d part of the string.
2- the unique and constant acceleration (a) in the simple machine is replaced in here with two different and variable accelerations whose ratio is however constant.
3- In the simple machine the constant acceleration makes plotting and animation of the system a straightforward procedure according to
s = (1/2)*at^2.However in the modified Atwood machine that we present in here the accelerations being variable there is no way to get the displacement as a direct function of time. This seems to make plotting & animation an impossible task. However we were able to devise a trick to overcome this difficulty.<img src="https://www.maplesoft.com/view.aspx?si=154598/Modified_Atwood_Machine.jpg" alt="Atwood Machine" style="max-width: 25%;" align="left"/>The following is a detailed study of the motion of an unconventional Atwood Machine where one mass is constrained to move along a fixed vertical axis.
The differences with the regular Atwood Machine are :
1- the tension T on the string on either side of the pulley though it is the same, however it is not constant in the present case because of the obliquity of the 2d part of the string.
2- the unique and constant acceleration (a) in the simple machine is replaced in here with two different and variable accelerations whose ratio is however constant.
3- In the simple machine the constant acceleration makes plotting and animation of the system a straightforward procedure according to
s = (1/2)*at^2.However in the modified Atwood machine that we present in here the accelerations being variable there is no way to get the displacement as a direct function of time. This seems to make plotting & animation an impossible task. However we were able to devise a trick to overcome this difficulty.https://www.maplesoft.com/applications/view.aspx?SID=154598&ref=FeedSat, 25 Jan 2020 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudySystem of Equations 2x2 and 3x3
https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=Feed
This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154520/sis_eq_dpd.png" alt="System of Equations 2x2 and 3x3" style="max-width: 25%;" align="left"/>This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=FeedTue, 19 Mar 2019 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloLinear Optimization Examples
https://www.maplesoft.com/applications/view.aspx?SID=154517&ref=Feed
So, this was introduced into my son's high school Precalculus I class, and he really didn't understand it. After reading his textbook, I could understand why, the explanation was terrible. So, I decided to do a few examples for him, to show him how it would work. While I used Maple to do the computational pieces, I didn't use any built-in functions, I kept it as simple as possible.<img src="https://www.maplesoft.com/view.aspx?si=154517/b0e3e02e0b878253dcb11a11a2b75fce.gif" alt="Linear Optimization Examples" style="max-width: 25%;" align="left"/>So, this was introduced into my son's high school Precalculus I class, and he really didn't understand it. After reading his textbook, I could understand why, the explanation was terrible. So, I decided to do a few examples for him, to show him how it would work. While I used Maple to do the computational pieces, I didn't use any built-in functions, I kept it as simple as possible.https://www.maplesoft.com/applications/view.aspx?SID=154517&ref=FeedTue, 19 Feb 2019 05:00:00 ZProf. Peter SchochProf. Peter SchochPlane flying through a thundercloud, calculating the E field
https://www.maplesoft.com/applications/view.aspx?SID=154519&ref=Feed
This problem models a thundercloud by a +40C charge at 10km height, -40C charge at 5km height and a 10C charge at a 2km height. It then has an airplane flying at 8km through the cloud. The crux of the problem is to calculate the Electric field on the plane beginning at the left of the cloud through to the right of the coud.
I placed the y axis along the charges within the cloud. his means the airplane has a fixed y value and just changes in x. I also numbered the charges from bottom to the top.<img src="https://www.maplesoft.com/view.aspx?si=154519/b9715d1a184de2946329d1d396866539.gif" alt="Plane flying through a thundercloud, calculating the E field" style="max-width: 25%;" align="left"/>This problem models a thundercloud by a +40C charge at 10km height, -40C charge at 5km height and a 10C charge at a 2km height. It then has an airplane flying at 8km through the cloud. The crux of the problem is to calculate the Electric field on the plane beginning at the left of the cloud through to the right of the coud.
I placed the y axis along the charges within the cloud. his means the airplane has a fixed y value and just changes in x. I also numbered the charges from bottom to the top.https://www.maplesoft.com/applications/view.aspx?SID=154519&ref=FeedTue, 19 Feb 2019 05:00:00 ZProf. Peter SchochProf. Peter SchochPlot of curvature and radius of curvature
https://www.maplesoft.com/applications/view.aspx?SID=154486&ref=Feed
This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.<img src="https://www.maplesoft.com/view.aspx?si=154486/radcurv.png" alt="Plot of curvature and radius of curvature" style="max-width: 25%;" align="left"/>This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.https://www.maplesoft.com/applications/view.aspx?SID=154486&ref=FeedMon, 03 Sep 2018 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloSolving 2nd Order Differential Equations
https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=Feed
This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.<img src="https://www.maplesoft.com/view.aspx?si=154426/2nd_order_des.PNG" alt="Solving 2nd Order Differential Equations" style="max-width: 25%;" align="left"/>This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonDE Phase Portraits - Animated Trajectories
https://www.maplesoft.com/applications/view.aspx?SID=154427&ref=Feed
This worksheet shows an animation of a phase portrait with three different trajectories, as well as animating distance plots.<img src="https://www.maplesoft.com/view.aspx?si=154427/phase_portrait.PNG" alt="DE Phase Portraits - Animated Trajectories" style="max-width: 25%;" align="left"/>This worksheet shows an animation of a phase portrait with three different trajectories, as well as animating distance plots.https://www.maplesoft.com/applications/view.aspx?SID=154427&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSolving ODEs using Maple: An Introduction
https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=Feed
In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.<img src="https://www.maplesoft.com/view.aspx?si=154422/ode.PNG" alt="Solving ODEs using Maple: An Introduction" style="max-width: 25%;" align="left"/>In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=FeedFri, 23 Mar 2018 04:00:00 ZDr. Francis PoulinDr. Francis PoulinKinematics Curvilinear
https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=Feed
With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154269/kc.png" alt="Kinematics Curvilinear" style="max-width: 25%;" align="left"/>With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=FeedTue, 14 Nov 2017 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of equation impulse-momentum
https://www.maplesoft.com/applications/view.aspx?SID=154347&ref=Feed
In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154347/mivis.png" alt="Plot of equation impulse-momentum" style="max-width: 25%;" align="left"/>In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154347&ref=FeedTue, 17 Oct 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMoment of a force using vectors
https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=Feed
The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154345/moment of force.PNG" alt="Moment of a force using vectors" style="max-width: 25%;" align="left"/>The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=FeedTue, 26 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloVector space with projections and forces
https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=Feed
With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" style="max-width: 25%;" align="left"/>With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=FeedMon, 11 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDisplacement and distance traveled with vectors
https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=Feed
In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" style="max-width: 25%;" align="left"/>In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=FeedMon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloClassroom Tips and Techniques: The Partial Fraction Decomposition
https://www.maplesoft.com/applications/view.aspx?SID=1753&ref=Feed
The algebraic technique of partial fraction decomposition typically appears first in the integral calculus course as part of the methodology of integrating rational functions; and second, in any course such as differential equations where Laplace transforms must be inverted. If the Laplace transform is used in an engineering course, partial fraction decompositions must generally be implemented over the complex field so that all factors are linear.
This column describes how to obtain the partial fraction decomposition in Maple, either with irreducible quadratic factors or with strictly linear factors. We also suggest some pedagogic devices for providing insight into the algebraic processes involved.<img src="https://www.maplesoft.com/view.aspx?si=1753/partialfrac.PNG" alt="Classroom Tips and Techniques: The Partial Fraction Decomposition" style="max-width: 25%;" align="left"/>The algebraic technique of partial fraction decomposition typically appears first in the integral calculus course as part of the methodology of integrating rational functions; and second, in any course such as differential equations where Laplace transforms must be inverted. If the Laplace transform is used in an engineering course, partial fraction decompositions must generally be implemented over the complex field so that all factors are linear.
This column describes how to obtain the partial fraction decomposition in Maple, either with irreducible quadratic factors or with strictly linear factors. We also suggest some pedagogic devices for providing insight into the algebraic processes involved.https://www.maplesoft.com/applications/view.aspx?SID=1753&ref=FeedFri, 25 Aug 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Eigenvalue Problems for ODEs
https://www.maplesoft.com/applications/view.aspx?SID=4971&ref=Feed
Some boundary value problems for partial differential equations are amenable to analytic techniques. For example, the constant-coefficient, second-order linear equations called the heat, wave, and potential equations are solved with some type of Fourier series representation obtained from the Sturm-Liouville eigenvalue problem that arises upon separating variables. The role of Maple in the solution of such boundary value problems is examined. Efficient techniques for separating variables, and a way to guide Maple through the solution of the resulting Sturm-Liouville eigenvalue problems are shown.<img src="https://www.maplesoft.com/view.aspx?si=4971/R-23EigenvalueProblemsforODEs.jpg" alt="Classroom Tips and Techniques: Eigenvalue Problems for ODEs" style="max-width: 25%;" align="left"/>Some boundary value problems for partial differential equations are amenable to analytic techniques. For example, the constant-coefficient, second-order linear equations called the heat, wave, and potential equations are solved with some type of Fourier series representation obtained from the Sturm-Liouville eigenvalue problem that arises upon separating variables. The role of Maple in the solution of such boundary value problems is examined. Efficient techniques for separating variables, and a way to guide Maple through the solution of the resulting Sturm-Liouville eigenvalue problems are shown.https://www.maplesoft.com/applications/view.aspx?SID=4971&ref=FeedMon, 14 Aug 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezPlot of Position Vector
https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=Feed
This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" style="max-width: 25%;" align="left"/>This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=FeedThu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloClassroom Tips and Techniques: Green's Functions for Second-Order ODEs
https://www.maplesoft.com/applications/view.aspx?SID=4820&ref=Feed
<p>For second-order ODEs, we compute the Green's function for both initial and boundary value problems. For the boundary value problem, we consider mixed and unmixed boundary conditions, of both homogeneous and nonhomogeneous types. In every case, we compare our solutions to direct solutions using Maple's dsolve command.</p><img src="https://www.maplesoft.com/view.aspx?si=4820/image.php.gif" alt="Classroom Tips and Techniques: Green's Functions for Second-Order ODEs" style="max-width: 25%;" align="left"/><p>For second-order ODEs, we compute the Green's function for both initial and boundary value problems. For the boundary value problem, we consider mixed and unmixed boundary conditions, of both homogeneous and nonhomogeneous types. In every case, we compare our solutions to direct solutions using Maple's dsolve command.</p>https://www.maplesoft.com/applications/view.aspx?SID=4820&ref=FeedTue, 04 Jul 2017 04:00:00 ZDr. Robert LopezDr. Robert Lopez