In Meteorology, it is relatively common to define a coordinate system in a rotated pole equi-rectangular projection, such that the x and y coordinate space are always orthogonal and which increase monotonically. As a result, there is a convenience class in Cartopy which wraps up the functionality:
import cartopy.crs as ccrs
gmp_2010 = ccrs.RotatedPole(pole_longitude=72.21, pole_latitude=80.08)
import matplotlib.pyplot as plt
plt.figure(figsize=(14, 14))
ax = plt.axes(projection=gmp_2010)
ax.coastlines()
ax.gridlines()
plt.show()
If we wanted to compare this coordinate system to the PlateCarree (equirectangular with a pole at 0, 90) we can see the difference in the gridlines:
import matplotlib.pyplot as plt
plt.figure(figsize=(14, 14))
ax1 = plt.subplot(1, 2, 1, projection=ccrs.NorthPolarStereo())
ax1.coastlines()
ax1.gridlines(gmp_2010, color='red')
ax1 = plt.subplot(1, 2, 2, projection=ccrs.NorthPolarStereo())
ax1.coastlines()
ax1.gridlines()
plt.show()