From 98ea87adcbb9873aa79b20b13f19d9f85ec2d846 Mon Sep 17 00:00:00 2001
From: Connor Johnstone <connor.johnstone@orionspace.com>
Date: Wed, 15 Mar 2023 15:50:47 -0600
Subject: [PATCH] Updated readme example to make more sense

---
 readme.md  | 24 ++++++++++++++----------
 src/lib.rs | 23 +++++++++++++----------
 2 files changed, 27 insertions(+), 20 deletions(-)

diff --git a/readme.md b/readme.md
index 75a5bf8..6ea1cc2 100644
--- a/readme.md
+++ b/readme.md
@@ -33,26 +33,30 @@ and field line tracing:
 For now, here is a simple example of using the propagator to solve a simple system:
 
 ```rust
-use nalgebra::Vector3;
+use nalgebra::Vector2;
 use differential_equations::prelude::*;
+use std::f64::consts::PI;
 
 // Define the system (parameters, derivative, and initial state)
-type Params = (f64, bool);
-let params = (34.0, true);
+type Params = (f64, f64); // Gravity and Length of Pendulum
+let params = (9.81, 1.0);
 
-fn derivative(t: f64, y: Vector3<f64>, p: &Params) -> Vector3<f64> {
-  if p.1 { -y } else { y * t }
+fn derivative(_t: f64, y: Vector2<f64>, p: &Params) -> Vector2<f64> {
+    let &(g, l) = p;
+    let theta = y[0];
+    let d_theta = y[1];
+    Vector2::new( d_theta, -(g/l) * theta.sin() )
 }
 
-let y0 = Vector3::new(1.0, 1.0, 1.0);
+let y0 = Vector2::new(0.0, PI/2.0);
 
 // Set up the problem (ODE, Integrator, Controller, and Callbacks)
-let ode = ODE::new(&derivative, 0.0, 10.0, y0, params);
-let dp45 = DormandPrince45::new(1e-12_f64, 1e-5_f64);
+let ode = ODE::new(&derivative, 0.0, 6.3, y0, params);
+let dp45 = DormandPrince45::new(1e-12_f64, 1e-6_f64);
 let controller = PIController::default();
 
 let value_too_high = Callback {
-  event: &|_: f64, y: Vector3<f64>, _: &Params| { 10.0 - y[0] },
+    event: &|t: f64, _y: Vector2<f64>, _p: &Params| { 5.0 - t },
     effect: &stop,
 };
 
@@ -61,5 +65,5 @@ let mut problem = Problem::new(ode, dp45, controller).with_callback(value_too_hi
 let solution = problem.solve();
 
 // Can interpolate solutions to whatever you want
-let interpolated_answer = solution.interpolate(8.2);
+let _interpolated_answer = solution.interpolate(4.4);
 ```
diff --git a/src/lib.rs b/src/lib.rs
index 02798ff..8ee27ec 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -16,7 +16,7 @@ pub mod prelude {
 
 #[cfg(test)]
 mod tests {
-    use nalgebra::{Vector3, Vector6};
+    use nalgebra::{Vector2, Vector6};
     use approx::assert_relative_eq;
     use crate::prelude::*;
     use std::f64::consts::PI;
@@ -24,22 +24,25 @@ mod tests {
     #[test]
     fn test_readme() {
         // Define the system (parameters, derivative, and initial state)
-        type Params = (f64, bool);
-        let params = (34.0, true);
+        type Params = (f64, f64); // Gravity and Length of Pendulum
+        let params = (9.81, 1.0);
 
-        fn derivative(t: f64, y: Vector3<f64>, p: &Params) -> Vector3<f64> {
-          if p.1 { -y } else { y * t }
+        fn derivative(_t: f64, y: Vector2<f64>, p: &Params) -> Vector2<f64> {
+            let &(g, l) = p;
+            let theta = y[0];
+            let d_theta = y[1];
+            Vector2::new( d_theta, -(g/l) * theta.sin() )
         }
 
-        let y0 = Vector3::new(1.0, 1.0, 1.0);
+        let y0 = Vector2::new(0.0, PI/2.0);
 
         // Set up the problem (ODE, Integrator, Controller, and Callbacks)
-        let ode = ODE::new(&derivative, 0.0, 10.0, y0, params);
-        let dp45 = DormandPrince45::new(1e-12_f64, 1e-5_f64);
+        let ode = ODE::new(&derivative, 0.0, 6.3, y0, params);
+        let dp45 = DormandPrince45::new(1e-12_f64, 1e-6_f64);
         let controller = PIController::default();
 
         let value_too_high = Callback {
-            event: &|_: f64, y: Vector3<f64>, _: &Params| { 10.0 - y[0] },
+            event: &|t: f64, _y: Vector2<f64>, _p: &Params| { 5.0 - t },
             effect: &stop,
         };
 
@@ -48,7 +51,7 @@ mod tests {
         let solution = problem.solve();
 
         // Can interpolate solutions to whatever you want
-        let _interpolated_answer = solution.interpolate(8.2);
+        let _interpolated_answer = solution.interpolate(4.4);
     }
 
     #[test]