J. M. Redwood: New Applications
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en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 31 Jan 2015 08:34:55 GMTSat, 31 Jan 2015 08:34:55 GMTNew applications published by J. M. Redwoodhttp://www.mapleprimes.com/images/mapleapps.gifJ. M. Redwood: New Applications
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Dynamics in Spherical Coordinates
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A brief introduction to dynamics in spherical coordinates.<img src="/view.aspx?si=4892/Dynamics in Spherical Coords Sketch 1.jpg" alt="Dynamics in Spherical Coordinates" align="left"/>A brief introduction to dynamics in spherical coordinates.4892Thu, 05 Apr 2007 00:00:00 ZJ. M. RedwoodJ. M. RedwoodStroud System of Units
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Before the International System (SI) of units came into use, there was great scope for errors when solving problems in mechanics. Professor H. Stroud, a physicist and chemist, devised a system for eliminating such errors during the late 1880s while teaching dynamics at Imperial College, London. This worksheet describes Professor Stroud's system for handling units and illustrates it with an example.<img src="/view.aspx?si=1447//applications/images/app_image_blank_lg.jpg" alt="Stroud System of Units" align="left"/>Before the International System (SI) of units came into use, there was great scope for errors when solving problems in mechanics. Professor H. Stroud, a physicist and chemist, devised a system for eliminating such errors during the late 1880s while teaching dynamics at Imperial College, London. This worksheet describes Professor Stroud's system for handling units and illustrates it with an example.1447Wed, 16 Mar 2005 00:00:00 ZJ. M. RedwoodJ. M. RedwoodMIT Servo
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This worksheet derives the loop transfer function of a tacho feedback compensated servo. It then plots the servo's Nyquist diagram, Bode diagrams, and closed loop responses to sinusoidal and unit step inputs with servo constants chosen to minimize noise in the input.<img src="/view.aspx?si=4769/MITServo_29.gif" alt="MIT Servo" align="left"/>This worksheet derives the loop transfer function of a tacho feedback compensated servo. It then plots the servo's Nyquist diagram, Bode diagrams, and closed loop responses to sinusoidal and unit step inputs with servo constants chosen to minimize noise in the input.4769Thu, 09 Dec 2004 00:00:00 ZJ. M. RedwoodJ. M. RedwoodSeries Compensation Design Using the Root Locus
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This worksheet illustrates a method for designing a series-compensation network for a simple servo. The method involves altering the root locus of a servo by siting the network's poles and zeros in the complex plane so that the locus passes through dominant poles that produce the desired response. The compensated servo's responses to standard inputs are then compared with those of the uncompensated servo. Finally, the network is designed using standard components and the compensated servo's performance is checked using these components.<img src="/view.aspx?si=4768/appviewer.aspx.gif" alt="Series Compensation Design Using the Root Locus" align="left"/>This worksheet illustrates a method for designing a series-compensation network for a simple servo. The method involves altering the root locus of a servo by siting the network's poles and zeros in the complex plane so that the locus passes through dominant poles that produce the desired response. The compensated servo's responses to standard inputs are then compared with those of the uncompensated servo. Finally, the network is designed using standard components and the compensated servo's performance is checked using these components.4768Thu, 09 Dec 2004 00:00:00 ZJ. M. RedwoodJ. M. RedwoodAnalysis of a Dual-Input, Multi-Loop Servo
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This worksheet derives the loop transfer function of a tacho feedback compensated servo. It plots the servo's Nyquist diagram, Bode diagrams, and closed loop responses to sinusoidal and unit step inputs.<img src="/view.aspx?si=3739/331.jpg" alt="Analysis of a Dual-Input, Multi-Loop Servo" align="left"/>This worksheet derives the loop transfer function of a tacho feedback compensated servo. It plots the servo's Nyquist diagram, Bode diagrams, and closed loop responses to sinusoidal and unit step inputs.3739Wed, 01 Sep 2004 00:00:00 ZJ. M. RedwoodJ. M. RedwoodLord Rayleigh's Principle
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The principle enunciated by Lord Rayleigh (1842 - 1919), physicist and mathematician, may be stated as: "The distribution of the potential and kinetic energies of a conservative, elastic system in the fundamental mode of vibration is such that the frequency is a minimum." This worksheet uses two examples of a vibrating elastic string to illustrate Lord Rayleigh's principle for estimating the fundamental frequency. <img src="/view.aspx?si=4492//applications/images/app_image_blank_lg.jpg" alt="Lord Rayleigh's Principle" align="left"/>The principle enunciated by Lord Rayleigh (1842 - 1919), physicist and mathematician, may be stated as: "The distribution of the potential and kinetic energies of a conservative, elastic system in the fundamental mode of vibration is such that the frequency is a minimum." This worksheet uses two examples of a vibrating elastic string to illustrate Lord Rayleigh's principle for estimating the fundamental frequency. 4492Thu, 25 Mar 2004 14:01:54 ZJ. M. RedwoodJ. M. RedwoodFitting a Strength Function by the Levenberg-Marquardt Method
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Procedure mnlfit , based on the Levenberg-Marquardt method, is used to fit a function relating adhesive bond strength to three variables. The maximum strength and values of the variables to produce it are estimated.<img src="/view.aspx?si=4160//applications/images/app_image_blank_lg.jpg" alt="Fitting a Strength Function by the Levenberg-Marquardt Method" align="left"/>Procedure mnlfit , based on the Levenberg-Marquardt method, is used to fit a function relating adhesive bond strength to three variables. The maximum strength and values of the variables to produce it are estimated.4160Mon, 05 Nov 2001 10:40:45 ZJ. M. RedwoodJ. M. RedwoodLogistic Cost Curve by the Levenberg-Marquardt Method
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Procedure mnlfit , based on the Levenberg-Marquardt method, is used to fit a Logistic function to a project's cost data and provide a means for estimating cash flows in similar projects.<img src="/view.aspx?si=4159//applications/images/app_image_blank_lg.jpg" alt="Logistic Cost Curve by the Levenberg-Marquardt Method" align="left"/>Procedure mnlfit , based on the Levenberg-Marquardt method, is used to fit a Logistic function to a project's cost data and provide a means for estimating cash flows in similar projects.4159Mon, 05 Nov 2001 10:38:22 ZJ. M. RedwoodJ. M. RedwoodHammerhead crane lifting heavy loads
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A compound oscillator, comprising two masses and two springs, is used to model the response of a big hammerhead crane and its load if one of its two reeves of steel wire ropes were to fail. The response is used to obtain a "back of the envelope" estimate of how far the load would fall, and check that the crane would not be overstressed.<img src="/view.aspx?si=3492//applications/images/app_image_blank_lg.jpg" alt="Hammerhead crane lifting heavy loads" align="left"/>A compound oscillator, comprising two masses and two springs, is used to model the response of a big hammerhead crane and its load if one of its two reeves of steel wire ropes were to fail. The response is used to obtain a "back of the envelope" estimate of how far the load would fall, and check that the crane would not be overstressed.3492Mon, 18 Jun 2001 00:00:00 ZJ. M. RedwoodJ. M. Redwood