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Downloads
Views
Date
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Free Online Textbook
127
views
51
downloads
0
comments
1991-Carmine_Chicone-Ordinary Differential Equations with Applications
This is a complete text for a graduate level course. Hence there is much theory, but there is a chapter on applications with some sophisticated approaches and high level modeling of motion.
orbits
two mass system
atom
magnetic field
coupled pendulum
inverted pendulum
charged particle
Kepler motion
Potential Scenario
171
views
80
downloads
0
comments
2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics
This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.
projectile
air resistance
free fall
drag
harmonic oscillation
Modeling Scenario
258
views
377
downloads
0
comments
3-080-PendulumModeling-ModelingScenario
We lead students through building model for several pendulum configurations in motion and ask students to compare results.
pendulum
period
linearization
Modeling Scenario
513
views
178
downloads
0
comments
3-033-S-TimeUpTimeDown-ModelingScenario
We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.
projectile motion
apex
vertical motion
Potential Scenario
154
views
75
downloads
0
comments
2017-David_Morin-Oscillations
So needless to say, an understanding of oscillations is required for an understanding of waves.
damping
frequency response
resonance
oscillation
beats
underdamping
harmonic oscillators
over damping
critical damping
Potential Scenario
119
views
43
downloads
0
comments
1988- N_Koblitz-Problems that Teach the Obvious but Difficult
Four problems are presented and two of them involve differential equations. These involve projectile motion in one and two dimensions.
projectile motion
Modeling Scenario
246
views
142
downloads
0
comments
3-027-BobbingDropping-ModelingScenario
We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
drug resistance
directed
buoyancy
free fall
static equilibrium
displacement
Potential Scenario
169
views
67
downloads
0
comments
2017-Andras_Domokos-Differential Equations - Theory and Applications – Notes
This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
Newton's Second Law of Motion
Newton's Law of Cooling
biochemical reactions
Poiseuille’s Law
stopping distance
Potential Scenario
112
views
62
downloads
0
comments
2015-Peter_Cumber-Waggling pendulums and visualization in mechanics
This article describes an equation of motion for a waggling pendulum.
resonance
inverted pendulum
mechanics
damped pendulum
Potential Scenario
158
views
49
downloads
0
comments
2009-Reid-King-Pendulum Motion and Differential Equations
This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect real-world behavior.
pendulum
physical pendulum
Modeling Scenario
205
views
213
downloads
0
comments
3-095-ShotInWater-ModelingScenario
This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.
projectile motion
terminal velocity
projectile
water resistance
reduction of order
friction
air resistance
Potential Scenario
167
views
47
downloads
0
comments
2006-Matt_MacWilliams-Developing ODEs to Describe the Motion of a Paper Helicopter
This paper attempts to create a model that describes the motion of a paper helicopter using engineering, physical and statistical knowledge.
experimental design
helicopter
Potential Scenario
162
views
43
downloads
0
comments
2014-Brun-EtAl-An introduction to the mechanics of the lasso
Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane.
bifurcation
motion
lasso
rod model
rodeo
Potential Scenario
200
views
85
downloads
0
comments
2009-Peter-Howard-Modeling With ODE
This is a set of class notes rich in examples and ideas for modeling. There is some MatLab code in support of some of the activities.
rates
competition
population
epidemic
pendulum
carbon dating
reaction chemistry
mechanics
planetary motion
drag racing
Hamilton’s method
variational method
Potential Scenario
192
views
44
downloads
0
comments
1994-Roland_Minton-A Progression of Projectiles-Examples from Sports
There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,
sports
resistance
projectile
baseball
drag
linear resistance
quadratic resistance
tennis
Potential Scenario
133
views
73
downloads
0
comments
2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps
In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes.
Accelerometers
free fall
jump
trampoline
Article or Presentation
143
views
50
downloads
0
comments
2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
resistance
projectile motion
projectile
fluid
Mersenne
Free Online Textbook
239
views
75
downloads
0
comments
2011-Richard_Fitzpatrick-Newtonian_Dynamics
This 300 page text is packed with motivational physics. Indeed, Professor Fitzpatrick brings us to the origins of why differential equations are the dominant tools of mathematics in the study of motion.
modeling
textbook
physics
bifurcation
Modeling Scenario
792
views
372
downloads
1
comments
1-128-RocketFlight-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
resistance
Flight
Rocketry
mass
Newton's Second Law of Motion
thrust
Free Body Diagram
apex
rocket
Modeling Scenario
280
views
167
downloads
0
comments
3-045-RampBounce-ModelingScenario
Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile motion model of the ball bouncing off the ramp.
projectile motion
inclined ramp
coefficient of restitution
optimal angle
bounce
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