This simulation simulates motion along a constrained path, such as what a roller coaster would take (assuming it has safety wheels to keep it on the track in “up-side-down” situations, of course). The simulation offers a chance to explore a number of concepts associated with roller coaster physics, including conservation of energy, reaction forces, motion in a vertical plane and friction. There are a number of example tracks which can be accessed via the drop down menu on the bottom right. Each of the tracks may be modified by dragging the control points wwhich are visible when the simulation is paused. The user can also specify the coaster's initial speed (v0) which in turn affects the total energy of the coaster. The user can also input the strength of the aerodynamic friction force via the constant k. The friction force is given by Ff =-kv. The simulation tracks the roller coaster car's kinetic energy (KE), potential energy (PE) and total mechanical energy (TotalE) which is the sum of KE and PE. If the car is subject to friction, thermal energy (HeatE) is also tracked to represent the "lost" heat energy.

https://www.engineersedge.com/physic...ator_15502.htm

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https://www.engineersedge.com/physic...ator_15502.htm

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Explicit Second Order Calculus Differential Equation Graphing Simulator

https://www.engineersedge.com/math/e...tial_15501.htm

differential-simulation.png

https://www.engineersedge.com/math/e...tial_15501.htm

differential-simulation.png