From 3cecb59560ee3161cf8fbfb7987fc1add4e9ccf6 Mon Sep 17 00:00:00 2001
From: Alex Gebben Work <agebben@uwyo.edu>
Date: Thu, 19 Feb 2026 17:10:05 -0700
Subject: [PATCH] Added test to conceptualize hamiltonians (not used)

---
 Hamilton_Test.r | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 Hamilton_Test.r

diff --git a/Hamilton_Test.r b/Hamilton_Test.r
new file mode 100644
index 0000000..3125e27
--- /dev/null
+++ b/Hamilton_Test.r
@@ -0,0 +1,34 @@
+#Based on Conrad Examples (Natural Resource Economics)
+#Page 20
+#Hamiltonian Method, terminal time
+GET_Z <- function(lambda_2){
+	Z=(1-lambda_2)/2
+	return(Z)
+}
+GET_LAMBDA <- function(LAMBDA_2,Z){LAMBDA_2+Z^2}
+Z_RES <- c()
+LAMBDA_RES <- c()
+LAMBDA_RES[1] <- 0
+#Z_RES[10] <- 0
+for(i in 1:10){
+Z_RES[i] <- GET_Z(LAMBDA_RES[i])
+if(i<10){LAMBDA_RES[i+1] <- GET_LAMBDA(LAMBDA_RES[i],GET_Z(LAMBDA_RES[i]))}
+}
+Z_RES <- c(rev(Z_RES),0)
+LAMBDA_RES <- c(NA,rev(LAMBDA_RES))
+X_RES <- c()
+Y_RES <- c()
+C_X <- 1000
+for(i in 1:11){
+X_RES[i] <- C_X
+Y_RES[i] <- Z_RES[i]*C_X
+C_X <- C_X-Y_RES[i]
+}
+RES <- cbind(LAMBDA_RES,Z_RES,X_RES,Y_RES)
+plot(X_RES)
+lines(1:11,Y_RES)
+#Phase Plane Diagram
+plot(X_RES,LAMBDA_RES)
+#Page 22 Dynamic Programming, terminal time
+	#Bellmans Equation backward induction
+