From b2b2a7493fb4f8792020564d4f537bf558469cf2 Mon Sep 17 00:00:00 2001 From: Bryan Weber Date: Sun, 16 Jun 2024 14:39:22 -0400 Subject: [PATCH] Bump Dependencies and Update Equation (#28) * Bump dependencies and fix resulting errors * Improve equation formatting and add spelling words * More bumps! * Fix errors --- .vscode/settings.json | 64 +- .../orbital_elements_and_the_state_vector.py | 1 + .../planetary-arrival-flyby.md | 1 + .../comparison-of-bielliptic-and-hohmann.md | 1 + orbital-maneuvers/plane-change-example.md | 1 + orbital-maneuvers/single-impulse-example.md | 2 + pdm.lock | 1479 +++++++++-------- pyproject.toml | 4 +- the-n-body-problem/lagrange-points.md | 14 +- the-orbit-equation/hyperbolic_trajectory.py | 2 +- .../elliptical-orbit-example.md | 4 +- .../elliptical-orbit-time-in-shadow.md | 1 + .../hyperbolic-trajectory-example.md | 12 +- .../universal-variables.md | 4 +- 14 files changed, 860 insertions(+), 730 deletions(-) diff --git a/.vscode/settings.json b/.vscode/settings.json index 7aa38fd6..e74eab61 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -1,31 +1,39 @@ { - "cSpell.words": [ - "apoapsis", - "deorbit", - "Hohmann", - "Kármán", - "periapsis", - "semimajor", - "Storrs" - ], - "cSpell.ignoreWords": ["devcontainer"], - "cSpell.languageSettings": [ - { - // use with Markdown files - "languageId": "markdown", - "dictionaries": ["latex"], - // Exclude code - // "ignoreRegExpList": [ - // "\\$.*\\$", - // "\\$\\$([\\n\\(\\)]|[^(\\$\\$)])*\\$\\$", - // "`.*`", - // "```([\\n\\(\\)]|[^(\\$\\$)])*```", - // "\\{\\w+\\}`.+`", - // ":::\\{math\\}([\\n\\(\\)]|[^(\\$\\$)])*:::", - // "---([\\n\\(\\)]|[^(\\$\\$)])*---" - // ] - } + "cSpell.words": [ + "apoapse", + "apoapsis", + "deorbit", + "Hohmann", + "Kármán", + "Laguerre", + "periapsis", + "Prussing", + "semimajor", + "Semiminor", + "Storrs", + "Stumpff" + ], + "cSpell.ignoreWords": [ + "devcontainer" + ], + "cSpell.languageSettings": [ + { + // use with Markdown files + "languageId": "markdown", + "dictionaries": [ + "latex" ], - "editor.formatOnSave": true - + // Exclude code + // "ignoreRegExpList": [ + // "\\$.*\\$", + // "\\$\\$([\\n\\(\\)]|[^(\\$\\$)])*\\$\\$", + // "`.*`", + // "```([\\n\\(\\)]|[^(\\$\\$)])*```", + // "\\{\\w+\\}`.+`", + // ":::\\{math\\}([\\n\\(\\)]|[^(\\$\\$)])*:::", + // "---([\\n\\(\\)]|[^(\\$\\$)])*---" + // ] + } + ], + "editor.formatOnSave": true } diff --git a/classical-orbital-elements/scripts/orbital_elements_and_the_state_vector.py b/classical-orbital-elements/scripts/orbital_elements_and_the_state_vector.py index 58de8c44..0b3c5bd9 100644 --- a/classical-orbital-elements/scripts/orbital_elements_and_the_state_vector.py +++ b/classical-orbital-elements/scripts/orbital_elements_and_the_state_vector.py @@ -51,6 +51,7 @@ warnings.simplefilter("ignore") from myst_nb import glue + np.set_printoptions(legacy="1.25") glue("orbital-elements-radius", r, display=False) glue("orbital-elements-velocity", v, display=False) glue("orbital-elements-v_r", v_r, display=False) diff --git a/interplanetary-maneuvers/planetary-arrival-flyby.md b/interplanetary-maneuvers/planetary-arrival-flyby.md index eb250855..71379706 100644 --- a/interplanetary-maneuvers/planetary-arrival-flyby.md +++ b/interplanetary-maneuvers/planetary-arrival-flyby.md @@ -250,6 +250,7 @@ h_1 = np.sqrt(mu_sun * R_Neptune * (1 - e_1)) from functools import partial from myst_nb import glue as myst_glue glue = partial(myst_glue, display=False) +np.set_printoptions(legacy="1.25") glue("interplanetary-flyby-e_1", e_1) glue("interplanetary-flyby-h_1", h_1) ``` diff --git a/orbital-maneuvers/comparison-of-bielliptic-and-hohmann.md b/orbital-maneuvers/comparison-of-bielliptic-and-hohmann.md index 9bf893d5..8d98c064 100644 --- a/orbital-maneuvers/comparison-of-bielliptic-and-hohmann.md +++ b/orbital-maneuvers/comparison-of-bielliptic-and-hohmann.md @@ -41,6 +41,7 @@ v_3 = np.sqrt(mu / r_3) # km/s ```{code-cell} ipython3 :tags: [remove-cell] +np.set_printoptions(legacy="1.25") glue("moon_circle_velocity", v_1) glue("leo_circle_velocity", v_3) ``` diff --git a/orbital-maneuvers/plane-change-example.md b/orbital-maneuvers/plane-change-example.md index aec23d85..4cd95482 100644 --- a/orbital-maneuvers/plane-change-example.md +++ b/orbital-maneuvers/plane-change-example.md @@ -66,6 +66,7 @@ Delta_v_1 = Delta_v_1_LEO + Delta_v_1_GEO ```{code-cell} ipython3 :tags: [remove-cell] +np.set_printoptions(legacy="1.25") from functools import partial from myst_nb import glue as myst_glue glue = partial(myst_glue, display=False) diff --git a/orbital-maneuvers/single-impulse-example.md b/orbital-maneuvers/single-impulse-example.md index fdea5252..96db012a 100644 --- a/orbital-maneuvers/single-impulse-example.md +++ b/orbital-maneuvers/single-impulse-example.md @@ -29,6 +29,8 @@ from matplotlib.patches import Circle, Arc import numpy as np from myst_nb import glue +np.set_printoptions(legacy="1.25") + R_E = 6378 # km orbit_radius = 1000 # 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text = "CC-BY-SA-4.0" } +description = "A book for Orbital Mechanics" +version = "0.0.0" [tool.pdm] distribution = false diff --git a/the-n-body-problem/lagrange-points.md b/the-n-body-problem/lagrange-points.md index 9ed09303..a90fea31 100644 --- a/the-n-body-problem/lagrange-points.md +++ b/the-n-body-problem/lagrange-points.md @@ -294,8 +294,8 @@ def init(): def animate(pi_2): m_1 = -pi_2 m_2 = 1 - pi_2 - m1_line.set_data(m_1, 0) - m2_line.set_data(m_2, 0) + m1_line.set_data([m_1], [0]) + m2_line.set_data([m_2], [0]) x_2 = m_2 * cos y_2 = m_2 * sin x_1 = m_1 * cos @@ -306,11 +306,11 @@ def animate(pi_2): L_1 = newton(func=collinear_lagrange, x0=0, args=(pi_2,)) L_3 = newton(func=collinear_lagrange, x0=-1, args=(pi_2,)) L_4 = L_5 = 0.5 - pi_2 - L1_line.set_data(L_1, 0) - L2_line.set_data(L_2, 0) - L3_line.set_data(L_3, 0) - L4_line.set_data(L_4, np.sqrt(3) / 2) - L5_line.set_data(L_5, -np.sqrt(3) / 2) + L1_line.set_data([L_1], [0]) + L2_line.set_data([L_2], [0]) + L3_line.set_data([L_3], [0]) + L4_line.set_data([L_4], [np.sqrt(3) / 2]) + L5_line.set_data([L_5], [-np.sqrt(3) / 2]) equil.set_data([m_1, L_4, m_2, L_5, m_1], [0, np.sqrt(3) / 2, 0, -np.sqrt(3) / 2, 0]) ann.set_text(fr"$\pi_2$ = {pi_2:.4G}") diff --git a/the-orbit-equation/hyperbolic_trajectory.py b/the-orbit-equation/hyperbolic_trajectory.py index 6edd2377..2bf750a1 100644 --- a/the-orbit-equation/hyperbolic_trajectory.py +++ b/the-orbit-equation/hyperbolic_trajectory.py @@ -59,7 +59,7 @@ def init(): def animate(t): r = a * (e**2 - 1) / (1 + e * np.cos(t)) - point.set_data(-a - r_p + r * np.cos(t), r * np.sin(t)) + point.set_data([-a - r_p + r * np.cos(t)], [r * np.sin(t)]) ann.set_text(rf"$\nu$ = {np.degrees(t):.2F}°") return (point, ann) diff --git a/time-since-periapsis-and-keplers-equation/elliptical-orbit-example.md b/time-since-periapsis-and-keplers-equation/elliptical-orbit-example.md index 16d23e6c..34f293db 100644 --- a/time-since-periapsis-and-keplers-equation/elliptical-orbit-example.md +++ b/time-since-periapsis-and-keplers-equation/elliptical-orbit-example.md @@ -35,7 +35,6 @@ e = \frac{r_a - r_p}{r_a + r_p} ::: ```{code-cell} ipython3 -# %matplotlib notebook import numpy as np from scipy.optimize import newton @@ -51,6 +50,7 @@ e = (r_a - r_p)/(r_a + r_p) :tags: [remove-cell] from functools import partial from myst_nb import glue as myst_glue +np.set_printoptions(legacy="1.25") glue = partial(myst_glue, display=False) glue("ellipse-time-since-periapsis-e", e) ``` @@ -149,7 +149,7 @@ def kepler(E, M_e, e): def d_kepler_d_E(E, M_e, e): """The derivative of Kepler's equation, to be used in a Newton solver. - + Note that the argument M_e is unused, but must be present so the function arguments are consistent with the kepler function. """ diff --git a/time-since-periapsis-and-keplers-equation/elliptical-orbit-time-in-shadow.md b/time-since-periapsis-and-keplers-equation/elliptical-orbit-time-in-shadow.md index 23765a9d..a007d5d1 100644 --- a/time-since-periapsis-and-keplers-equation/elliptical-orbit-time-in-shadow.md +++ b/time-since-periapsis-and-keplers-equation/elliptical-orbit-time-in-shadow.md @@ -29,6 +29,7 @@ from matplotlib.patches import Ellipse, Circle, Arc, Rectangle import numpy as np glue = partial(myst_glue, display=False) +np.set_printoptions(legacy="1.25") mu = 3.986004418E5 # km**3/s**2 R_E = 6378 # km diff --git a/time-since-periapsis-and-keplers-equation/hyperbolic-trajectory-example.md b/time-since-periapsis-and-keplers-equation/hyperbolic-trajectory-example.md index 54fe57c5..68cef494 100644 --- a/time-since-periapsis-and-keplers-equation/hyperbolic-trajectory-example.md +++ b/time-since-periapsis-and-keplers-equation/hyperbolic-trajectory-example.md @@ -41,6 +41,8 @@ e = h**2 / (r_p * mu) - 1 :tags: [remove-cell] from functools import partial from myst_nb import glue as myst_glue + +np.set_printoptions(legacy="1.25") glue = partial(myst_glue, display=False) glue("hyperbolic-time-since-perigee-h", h) @@ -117,7 +119,7 @@ def kepler(F, M_h, e): def d_kepler_d_F(F, M_h, e): """The derivative of Kepler's equation, to be used in a Newton solver. - + Note that the argument M_h is unused, but must be present so the function arguments are consistent with the kepler function. """ @@ -129,7 +131,7 @@ F_2 = newton(func=kepler, fprime=d_kepler_d_F, x0=np.pi, args=(M_h2, e)) With this value for $F$, we can calculate the value for $\nu$. To avoid quadrant ambiguity problems, we will use Eq. {eq}`eq:eccentric-anomaly-true-anomaly-hyperbola`. ```{code-cell} ipython3 -sqrt_e = np.sqrt((e + 1) / (e - 1)) +sqrt_e = np.sqrt((e + 1) / (e - 1)) nu_2 = (2 * np.arctan(sqrt_e * np.tanh(F_2 / 2))) % (2 * np.pi) ``` @@ -181,12 +183,12 @@ function kepler v_p = 15; % km/s h = r_p * v_p; e = h^2 / (mu * r_p) - 1; - + nu_1 = deg2rad(100); F_1 = 2 * atanh(sqrt((e - 1) / (e + 1)) * tan(nu_1 / 2)); M_h1 = e * sinh(F_1) - F_1; t_1 = h^3 / mu^2 * 1 / (e^2 - 1)^(3 / 2) * M_h1; - + t_2 = t_1 + 3 * 3600; M_h2 = mu^2 / h^3 * (e^2 - 1)^(3 / 2) * t_2; @@ -198,7 +200,7 @@ function kepler t2 = 2 * atan(sqrt((e + 1) / (e - 1)) * tanh(F_2 / 2)); nu_2 = mod(t2, 2 * pi); disp(rad2deg(nu_2)) - + r_2 = h^2 / mu * 1 / (1 + e * cos(nu_2)); v_perp = h / r_2; v_r = mu / h * e * sin(nu_2); diff --git a/time-since-periapsis-and-keplers-equation/universal-variables.md b/time-since-periapsis-and-keplers-equation/universal-variables.md index c8ef22aa..211441d0 100644 --- a/time-since-periapsis-and-keplers-equation/universal-variables.md +++ b/time-since-periapsis-and-keplers-equation/universal-variables.md @@ -306,13 +306,13 @@ Alternatively, a more refined estimate can be determined using a secant estimate where $f(\chi^{+})$ is the solution of Kepler's equation with the $\chi^{+}$ value. ::::{note} -Prussing and Conway {cite}`Prussing2013`, citing Conway {cite}`Conway1986` suggest that faster convergence in the solution of Kepler's equation can be achieved by using the **Laguerre algorithm**, rather than Newton's algorithm. Another advantage of the Laguerre algorithm is that it is relatively insensitive to the value of the initial guess. +Prussing and Conway {cite}`Prussing2013`, citing Conway {cite}`Conway1986` suggest that faster convergence in the solution of Kepler's equation can be achieved by using the [**Laguerre algorithm**](https://en.wikipedia.org/wiki/Laguerre%27s_method), rather than Newton's algorithm. Another advantage of the Laguerre algorithm is that it is relatively insensitive to the value of the initial guess. The Laguerre algorithm can be implemented as: :::{math} :label: -\chi_{i + 1} = \chi_{i} - \frac{n f(\chi_i)}{f'(\chi_i) \pm \left[\left(n - 1\right)^2 \left(f'(\chi_i)\right)^2 - n\left(n - 1\right) f(\chi_i)f''(\chi_i)\right]^{1/2}} +\chi_{i + 1} = \chi_{i} - \frac{n f(\chi_i)}{f'(\chi_i) \pm \sqrt{\left(n - 1\right)^2 \left[f'(\chi_i)\right]^2 - n\left(n - 1\right) f(\chi_i)f''(\chi_i)}} ::: The sign ambiguity in the denominator is determined by taking the sign of the numerical value of $f'(\chi_i)$. In addition, the solution is relatively insensitive to the choice of the value of $n$, which is an integer constant. It seems as though $n = 5$ is a reasonable value. Choosing $n = 1$ gives the standard Newton's algorithm.