This tutorial derives the formulas of a projectile model taking into account the aerodynamic drag. A finite differences numerical method is used. Though fairly easy to apply and understand, this type of methods can solve much more complex problems than the high-school type approach shown in the previous tutorials. An Excel model will be implemented in the next section. Projectile MotionContinue Reading

Now that we have a simple animated projectile motion (previous tutorial) let’s try to add on the chart the three instantaneous speed vectors associated with the projectile. These speed vectors are: the horizontal speed, vertical speed and the total speed vector. The model works in all Excel versions but in 2007 it’s rather slow. [sociallocker][/sociallocker] Projectile Motion Tutorial #3 –Continue Reading

Hi Folks, As a kid was fascinated with high power rifles, sniper rifles, cannons and in general, fast projectiles.  I’ve been brainwashed with all sorts of urban legends about how far an AK 47 or a pistol can shoot or how thick a steel metal plate a bullet can penetrate at various distances. I’ve also watched some documentary about snipersContinue Reading

Here is the third part of a tutorial in both elementary dynamics and numerical methods. It is written at a basic level and it shows you how to set up a dynamic model for numerical solving of simple differential equations. The dynamic model makes use of an infinite loop, which make the calculations advance in time. Instead of a large tableContinue Reading

Here is the second part of a tutorial in both elementary dynamics and numerical methods. It is written at a  basic level and it shows you how to solve a system of difference equations in an Excel table. It also starts to explain how to animate the model. [sociallocker][/sociallocker] A casual approach to numerical modeling – the Spring-Mass-Damper System – part 2.Continue Reading

Here is the first part of a casual tutorial in both elementary dynamics and numerical methods. It is written at a very basic level and it shows you how to solve a system of difference equations with a pencil and a paper and perhaps a pocket calculator to speed things up. A casual approach to numerical modeling – the Spring-Mass-Damper-System –Continue Reading

Hi guys, here is the second part of a tutorial describing the matematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section describes the kinematic equations involved in the articulated linkage mechanism on the top of the table, the custom spreadsheet functions used in the model and some overallContinue Reading

Hi guys, here is the first part of a tutorial describing the mathematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section refers only to the kinematic equations for the movement of three pendulums. A second section will be published later and it will describe the kinematic equations involved inContinue Reading

Hi! Here is an improved (faster and cleaner) version of the harmonograph. The worksheet has three different areas, the physical machine (a photo of the machine build out of wood by Karl Sims), the virtual machine (which is a 2D chart with a top view of a model showing the three pendulum ends, the drawing table, and the linkage mechanism which connects pendulum #1,Continue Reading

Hi folks, as a continuation to the previous tutorial here is a 3-body planetary model where the solution to the equations is contained in a static form, as a lookup table (I previously called it a “pure spreadsheet solution”). The model is static in the sense that after any parameter is changed, the solution data remains unchanged in a table until a new parameter is updated by theContinue Reading

Here is a tutorial explaining how to model a two dimensional  2-body planetary system in Excel. It uses the Euler method of integration. The tutorial starts with explaining the simple Newtonian laws acting on the two planets. There are essentially just two forces acting on each body at any time: the inertia and the gravitational attraction. During each small time step,Continue Reading

Hi there, this is a tutorial explaining the construction of a very basic Lissajous emulator in Excel. It’s supposed to be very easy to understand at the high school level. Good luck, George [sociallocker][/sociallocker] A Lissajous emulator in Excel by George Lungu   Introduction: Jules A. Lissajous was a French mathematician from the 19th century – He wanted to visualizeContinue Reading