Given
x = x_c * chi
t = t_c * tau
expressing dx/dt in chi, tau is: x_c/t_c * dchi / dtau
https://www.wikiwand.com/en/Nondimensionalization#Conventions
How to evaluate the dx/dt change of variables with sympy given x(chi), t(tau) expressions?
from sympy import symbols, diff
# Define the symbols
x, chi, x_c, t, tau, t_c = symbols('x chi x_c t tau t_c', real=True)
# Define the expressions for x and t in terms of chi and tau
x_expr = x_c * chi
t_expr = t_c * tau
x_expr.diff(t_expr)
results in the somewhat obvious error:
ValueError: Can't calculate derivative wrt t_c*tau.