From 23f9aad55b99e26fc755864a5cc29afd78c8e012 Mon Sep 17 00:00:00 2001 From: "John M. Penn" Date: Tue, 8 Sep 2015 17:05:37 -0500 Subject: [PATCH] Updates to SIM_cannon_analytic README --- trick_sims/SIM_cannon_analytic/README.md | 55 +++++++++--------- .../SIM_cannon_analytic/images/CannonInit.png | Bin 46490 -> 46380 bytes .../SIM_cannon_analytic/images/init_v_x_0.png | Bin 0 -> 824 bytes .../SIM_cannon_analytic/images/init_v_y_0.png | Bin 0 -> 844 bytes .../images/initial_vel_x.png | Bin 1086 -> 0 bytes .../images/initial_vel_y.png | Bin 1104 -> 0 bytes .../SIM_cannon_analytic/images/param_s.png | Bin 0 -> 373 bytes .../images/param_theta.png | Bin 0 -> 359 bytes .../images/solution_vx.png | Bin 0 -> 712 bytes .../images/solution_vy.png | Bin 0 -> 1084 bytes .../SIM_cannon_analytic/images/solution_x.png | Bin 846 -> 873 bytes .../SIM_cannon_analytic/images/solution_y.png | Bin 1269 -> 925 bytes .../images/time_of_impact.png | Bin 1569 -> 1794 bytes trick_sims/SIM_cannon_analytic/images/v_x.png | Bin 0 -> 569 bytes .../SIM_cannon_analytic/images/v_x_0.png | Bin 0 -> 433 bytes trick_sims/SIM_cannon_analytic/images/v_y.png | Bin 0 -> 586 bytes .../SIM_cannon_analytic/images/v_y_0.png | Bin 0 -> 464 bytes .../SIM_cannon_analytic/images/vector_v.png | Bin 0 -> 366 bytes .../SIM_cannon_analytic/images/vector_x.png | Bin 0 -> 372 bytes trick_sims/SIM_cannon_analytic/images/x_0.png | Bin 0 -> 406 bytes trick_sims/SIM_cannon_analytic/images/y_0.png | Bin 0 -> 409 bytes 21 files changed, 27 insertions(+), 28 deletions(-) create mode 100644 trick_sims/SIM_cannon_analytic/images/init_v_x_0.png create mode 100644 trick_sims/SIM_cannon_analytic/images/init_v_y_0.png delete mode 100644 trick_sims/SIM_cannon_analytic/images/initial_vel_x.png delete mode 100644 trick_sims/SIM_cannon_analytic/images/initial_vel_y.png create mode 100644 trick_sims/SIM_cannon_analytic/images/param_s.png create mode 100644 trick_sims/SIM_cannon_analytic/images/param_theta.png create mode 100644 trick_sims/SIM_cannon_analytic/images/solution_vx.png create mode 100644 trick_sims/SIM_cannon_analytic/images/solution_vy.png create mode 100644 trick_sims/SIM_cannon_analytic/images/v_x.png create mode 100644 trick_sims/SIM_cannon_analytic/images/v_x_0.png create mode 100644 trick_sims/SIM_cannon_analytic/images/v_y.png create mode 100644 trick_sims/SIM_cannon_analytic/images/v_y_0.png create mode 100644 trick_sims/SIM_cannon_analytic/images/vector_v.png create mode 100644 trick_sims/SIM_cannon_analytic/images/vector_x.png create mode 100644 trick_sims/SIM_cannon_analytic/images/x_0.png create mode 100644 trick_sims/SIM_cannon_analytic/images/y_0.png diff --git a/trick_sims/SIM_cannon_analytic/README.md b/trick_sims/SIM_cannon_analytic/README.md index def67196..c0e0325c 100644 --- a/trick_sims/SIM_cannon_analytic/README.md +++ b/trick_sims/SIM_cannon_analytic/README.md @@ -1,48 +1,47 @@ #SIM\_cannon\_analytic --- This is first of eight Trick-based simulations that one builds in the Trick -Tutorial (Section 3). It's purpose is to introduce the fundamentals of building -a Trick simulation. +Tutorial (Section 3). It's purpose is to introduce some of the fundamentals +of building a Trick simulation. -Here we simulate the flight of a cannon ball, given an initial position, and -velocity subject to the following assumptions and limitations: +Here we simulate the flight of a cannon ball. We want to know the position and velocity of the cannon ball over time, given an initial position, and +velocity, and subject to the following assumptions and limitations: * The **only** force acting on the cannon ball is gravity. * The acceleration of gravity (g) is constant and equal to -9.81 meters per second squared. * The surface of the ground is defined as where y=0. -![X(t) = Vx * t + X0](images/CannonInit.png) +![](images/CannonInit.png) --- -### Approach +### Solution -Since this problem has a closed-form solution, that's what we use : +This problem has a closed-form solution, so that's what is used. -![X(t) = Vx * t + X0](images/solution_x.png) +![v_{x0}=S\cos\theta](images/init_v_x_0.png) -![Y(t) = (1/2)gt^2 + Vy * t + Y0](images/solution_y.png) +![v_{y0}=S\sin\theta](images/init_v_y_0.png) -The time when the cannon ball impacts the ground is: +![](images/solution_vx.png) + +![](images/solution_vy.png) + +![](images/solution_x.png) + +![](images/solution_y.png) + +The cannon ball will impact the ground, when y(t)=0 at: ![](images/time_of_impact.png) --- -### Inputs -Variable | Type | Units ------------------------|----------------|------- -dyn.cannon.pos0 | double[2] | m -dyn.cannon.init\_angle | double | r -dyn.cannon.init\_speed | double | m/s -The initial velocity is : +### CANNON Object +Model Variable | Simulation Variable | Type | Units +--------------------------------------------|---------------------|---------|------- +![](images/x_0.png), ![](images/y_0.png) | CANNON.pos0[2] |double[2]| m +![](images/v_x_0.png), ![](images/v_y_0.png)| CANNON.vel0[2] |double[2]| m/s +![\theta](images/param_theta.png) | CANNON.init\_angle |double | r +![speed](images/param_s.png) | CANNON.init\_speed |double | m/s +![\vec{x}](images/vector_x.png) | CANNON.pos[2] |double[2]| m +![\vec{v}](images/vector_v.png) | CANNON.vel[2] |double[2]| m/s -![Vx = speed * cos(angle)](images/initial_vel_x.png), -![Vy = speed * sin(angle)](images/initial_vel_y.png) - --- -### Outputs 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