From 5474d8fb78b6b385954969cdfc89a72fd3d34808 Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Fri, 18 Aug 2023 15:18:16 +0000
Subject: [PATCH 1/7] build(deps): bump certifi from 2023.5.7 to 2023.7.22

Bumps [certifi](https://github.com/certifi/python-certifi) from 2023.5.7 to 2023.7.22.
- [Commits](https://github.com/certifi/python-certifi/compare/2023.05.07...2023.07.22)

---
updated-dependencies:
- dependency-name: certifi
  dependency-type: indirect
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 poetry.lock | 2066 ---------------------------------------------------
 1 file changed, 2066 deletions(-)
 delete mode 100644 poetry.lock

diff --git a/poetry.lock b/poetry.lock
deleted file mode 100644
index 8931e67e..00000000
--- a/poetry.lock
+++ /dev/null
@@ -1,2066 +0,0 @@
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From 46a50ae8c41ae2a5ba74063478cc465aeec7a340 Mon Sep 17 00:00:00 2001
From: Arman Tekinalp <53585636+armantekinalp@users.noreply.github.com>
Date: Tue, 5 Dec 2023 17:26:29 -0600
Subject: [PATCH 2/7] Update inquiry---need-help-for-my-project.md

---
 .github/ISSUE_TEMPLATE/inquiry---need-help-for-my-project.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/ISSUE_TEMPLATE/inquiry---need-help-for-my-project.md b/.github/ISSUE_TEMPLATE/inquiry---need-help-for-my-project.md
index 20e02b22..b3ce0c72 100644
--- a/.github/ISSUE_TEMPLATE/inquiry---need-help-for-my-project.md
+++ b/.github/ISSUE_TEMPLATE/inquiry---need-help-for-my-project.md
@@ -12,7 +12,7 @@ A clear description of your problem.
 
 **To Reproduce**
 - URL for project repository
-- Code implementation
+- Code implementation (If your code is long, please use Gist and share the link.)
 
 **Expected behavior**
 A clear and concise description of what you expected to happen.

From 52d6d5e010a520b516536e5930ef06fbb52426a6 Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Tue, 16 Jan 2024 20:49:53 +0000
Subject: [PATCH 3/7] build(deps): bump readthedocs-sphinx-search from 0.1.2 to
 0.3.2

Bumps [readthedocs-sphinx-search](https://github.com/readthedocs/readthedocs-sphinx-search) from 0.1.2 to 0.3.2.
- [Changelog](https://github.com/readthedocs/readthedocs-sphinx-search/blob/main/CHANGELOG.rst)
- [Commits](https://github.com/readthedocs/readthedocs-sphinx-search/compare/0.1.2...0.3.2)

---
updated-dependencies:
- dependency-name: readthedocs-sphinx-search
  dependency-type: direct:production
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 pyproject.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index 4e5f998d..942fa5b2 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -46,7 +46,7 @@ tqdm = "^4.61.1"
 # below `extras`. They can be opted into by apps.
 Sphinx = {version = "^6.1", optional = true}
 sphinx-book-theme = {version = "^1.0", optional = true}
-readthedocs-sphinx-search = {version = "^0.1.1", optional = true}
+readthedocs-sphinx-search = {version = ">=0.1.1,<0.4.0", optional = true}
 sphinx-autodoc-typehints = {version = "^1.21", optional = true}
 myst-parser = {version = "^1.0", optional = true}
 numpydoc = {version = "^1.3.1", optional = true}

From a24f88c949b991be26f934bce3694dda6bcd9350 Mon Sep 17 00:00:00 2001
From: Ali-7800 <47090295+Ali-7800@users.noreply.github.com>
Date: Thu, 22 Feb 2024 17:15:19 -0600
Subject: [PATCH 4/7] New: Catenary Case

---
 examples/CatenaryCase/catenary.py        | 129 +++++++++++++++++++++++
 examples/CatenaryCase/post_processing.py |  74 +++++++++++++
 examples/README.md                       |  32 +++---
 3 files changed, 222 insertions(+), 13 deletions(-)
 create mode 100644 examples/CatenaryCase/catenary.py
 create mode 100644 examples/CatenaryCase/post_processing.py

diff --git a/examples/CatenaryCase/catenary.py b/examples/CatenaryCase/catenary.py
new file mode 100644
index 00000000..e8f79671
--- /dev/null
+++ b/examples/CatenaryCase/catenary.py
@@ -0,0 +1,129 @@
+import numpy as np
+from elastica import *
+
+from post_processing import (
+    plot_video,
+    plot_catenary,
+)
+
+
+class CatenarySimulator(BaseSystemCollection, Constraints, Forcing, Damping, CallBacks):
+    pass
+
+
+catenary_sim = CatenarySimulator()
+final_time = 10
+damping_constant = 0.3
+time_step = 1e-4
+total_steps = int(final_time / time_step)
+rendering_fps = 20
+step_skip = int(1.0 / (rendering_fps * time_step))
+
+n_elem = 500
+
+start = np.zeros((3,))
+direction = np.array([1.0, 0.0, 0.0])
+normal = np.array([0.0, 0.0, 1.0])
+binormal = np.cross(direction, normal)
+
+# catenary parameters
+base_length = 1.0
+base_radius = 0.01
+base_area = np.pi * (base_radius ** 2)
+volume = base_area * base_length
+mass = 0.2
+density = mass / volume
+E = 1e4
+poisson_ratio = 0.5
+shear_modulus = E / (poisson_ratio + 1.0)
+
+base_rod = CosseratRod.straight_rod(
+    n_elem,
+    start,
+    direction,
+    normal,
+    base_length,
+    base_radius,
+    density,
+    youngs_modulus=E,
+    shear_modulus=shear_modulus,
+)
+
+catenary_sim.append(base_rod)
+
+# add damping
+catenary_sim.dampen(base_rod).using(
+    AnalyticalLinearDamper,
+    damping_constant=damping_constant,
+    time_step=time_step,
+)
+
+# Add gravity
+catenary_sim.add_forcing_to(base_rod).using(
+    GravityForces, acc_gravity=-9.80665 * normal
+)
+
+# fix catenary ends
+catenary_sim.constrain(base_rod).using(
+    FixedConstraint, constrained_position_idx=(0, -1), constrained_director_idx=(0, -1)
+)
+
+
+# Add call backs
+class CatenaryCallBack(CallBackBaseClass):
+    """
+    Call back function for continuum snake
+    """
+
+    def __init__(self, step_skip: int, callback_params: dict):
+        CallBackBaseClass.__init__(self)
+        self.every = step_skip
+        self.callback_params = callback_params
+
+    def make_callback(self, system, time, current_step: int):
+
+        if current_step % self.every == 0:
+
+            self.callback_params["time"].append(time)
+            self.callback_params["step"].append(current_step)
+            self.callback_params["position"].append(system.position_collection.copy())
+            self.callback_params["radius"].append(system.radius.copy())
+            self.callback_params["internal_force"].append(system.internal_forces.copy())
+
+            return
+
+
+pp_list = defaultdict(list)
+catenary_sim.collect_diagnostics(base_rod).using(
+    CatenaryCallBack, step_skip=step_skip, callback_params=pp_list
+)
+
+
+catenary_sim.finalize()
+
+
+timestepper = PositionVerlet()
+
+integrate(timestepper, catenary_sim, final_time, total_steps)
+position = np.array(pp_list["position"])
+b = np.min(position[-1][2])
+
+SAVE_VIDEO = True
+if SAVE_VIDEO:
+    # plotting the videos
+    filename_video = "catenary.mp4"
+    plot_video(
+        pp_list,
+        video_name=filename_video,
+        fps=rendering_fps,
+        xlim=[0, base_length],
+        ylim=[-0.5 * base_length, 0.5 * base_length],
+    )
+
+PLOT_RESULTS = True
+if PLOT_RESULTS:
+    plot_catenary(
+        pp_list,
+        xlim=(0, base_length),
+        ylim=(b, 0.0),
+    )
diff --git a/examples/CatenaryCase/post_processing.py b/examples/CatenaryCase/post_processing.py
new file mode 100644
index 00000000..9b695fca
--- /dev/null
+++ b/examples/CatenaryCase/post_processing.py
@@ -0,0 +1,74 @@
+import numpy as np
+import matplotlib
+
+matplotlib.use("Agg")  # Must be before importing matplotlib.pyplot or pylab!
+from matplotlib import pyplot as plt
+from tqdm import tqdm
+import scipy as sci
+
+
+def plot_video(
+    plot_params: dict,
+    video_name="video.mp4",
+    fps=15,
+    xlim=(0, 4),
+    ylim=(-1, 1),
+):
+    import matplotlib.animation as manimation
+
+    positions_over_time = np.array(plot_params["position"])
+
+    print("plot video")
+    FFMpegWriter = manimation.writers["ffmpeg"]
+    metadata = dict(title="Movie Test", artist="Matplotlib", comment="Movie support!")
+    writer = FFMpegWriter(fps=fps, metadata=metadata)
+    fig = plt.figure(figsize=(10, 8), frameon=True, dpi=150)
+    ax = fig.add_subplot(111)
+    ax.set_xlim(*xlim)
+    ax.set_ylim(*ylim)
+    ax.set_xlabel("x [m]", fontsize=16)
+    ax.set_ylabel("y [m]", fontsize=16)
+    # plt.axis("equal")
+    with writer.saving(fig, video_name, dpi=150):
+        rod_lines_2d = ax.plot(positions_over_time[0][2], positions_over_time[0][0])[0]
+        for time in tqdm(range(1, len(plot_params["time"]))):
+            rod_lines_2d.set_xdata(positions_over_time[time][0])
+            rod_lines_2d.set_ydata(positions_over_time[time][2])
+            writer.grab_frame()
+
+    # Be a good boy and close figures
+    # https://stackoverflow.com/a/37451036
+    # plt.close(fig) alone does not suffice
+    # See https://github.com/matplotlib/matplotlib/issues/8560/
+    plt.close(plt.gcf())
+
+
+def plot_catenary(plot_params: dict, xlim=(0, 1), ylim=(-0.5, 0.5), base_length=1.0):
+    matplotlib.use("TkAgg")
+    position = np.array(plot_params["position"])
+    n_elem = position.shape[-1]
+    lowest_point = np.min(position[-1][2])
+    x_catenary = np.linspace(0, base_length, 100)
+
+    def f_non_elastic_catenary(x):
+        return x * (1 - np.cosh(1 / (2 * x))) - lowest_point
+
+    a = sci.optimize.fsolve(f_non_elastic_catenary, x0=1.0)  # solve for a
+    y_catenary = a * np.cosh((x_catenary - 0.5) / a) - a * np.cosh(1 / (2 * a))
+    plt.plot(position[-1][0], position[-1][2], label="Simulation", linewidth=3)
+    plt.plot(
+        x_catenary,
+        y_catenary,
+        label="Catenary (Analytical Solution)",
+        linewidth=3,
+        linestyle="dashed",
+    )
+    plt.xlim(xlim)
+    plt.ylim(ylim)
+    plt.title("Catenary Final Shape")
+    plt.grid()
+    plt.legend()
+    plt.xlabel("x [m]", fontsize=16)
+    plt.ylabel("y [m]", fontsize=16)
+    plt.savefig("plot.png", dpi=300)
+    plt.show()
diff --git a/examples/README.md b/examples/README.md
index 489ea449..39f6ddce 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -26,17 +26,20 @@ Examples can serve as a starting template for customized usages.
     * __Purpose__: Physical convergence test of simple pendulum with flexible rod.
     * __Features__: CosseratRod, HingeBC, GravityForces
 * [ContinuumSnakeCase](./ContinuumSnakeCase)
-    * __Purpose__: Demonstrate simple case of modeling biological creature using PyElastica. The example use friction to create slithering snake, and optimize the speed using [CMA](https://github.com/CMA-ES/pycma).
-    * __Features__: CosseratRod, MuscleTorques, AnisotropicFrictionalPlane, Gravity, CMA Optimization
-    * [MuscularSnake](./MuscularSnake)
-      * __Purpose__: Example of [Parallel connection module](../elastica/experimental/connection_contact_joint/parallel_connection.py) and customized [Force module](./MuscularSnake/muscle_forces.py) to implement muscular snake.
-      * __Features__: MuscleForces(custom implemented)
+    * __Purpose__: Demonstrate simple case of modeling biological creature using PyElastica. The example uses friction to create slithering snake, and optimize the speed using [CMA](https://github.com/CMA-ES/pycma).
+    * __Features__: CosseratRod, MuscleTorques, RodPlaneContactWithAnisotropicFriction, Gravity, CMA Optimization
+* [ContinuumSnakeWithLiftingWaveCase](./ContinuumSnakeWithLiftingWaveCase)
+    * __Purpose__: Demonstrate simple case of modeling biological creature using PyElastica. The example uses friction to create slithering snake with lift.
+    * __Features__: CosseratRod, MuscleTorquesLifting(custom implemented), SnakeRodPlaneContact(custom implemented), Gravity
+* [MuscularSnake](./MuscularSnake)
+    * __Purpose__: Example of [Parallel connection module](../elastica/experimental/connection_contact_joint/parallel_connection.py) and customized [Force module](./MuscularSnake/muscle_forces.py) to implement muscular snake.
+    * __Features__: MuscleForces(custom implemented)
 * [ButterflyCase](./ButterflyCase)
     * __Purpose__: Demonstrate simple restoration with initial strain.
     * __Features__: CosseratRod
 * [FrictionValidationCases](./FrictionValidationCases)
     * __Purpose__: Physical validation of rolling and translational friction.
-    * __Features__: CosseratRod, UniformForces, AnisotropicFrictionalPlane
+    * __Features__: CosseratRod, UniformForces, RodPlaneContactWithAnisotropicFriction
 * [JointCases](./JointCases)
     * __Purpose__: Demonstrate various joint usage with Cosserat Rod.
     * __Features__: FreeJoint, FixedJoint, HingeJoint, OneEndFixedRod, EndpointForcesSinusoidal
@@ -45,27 +48,27 @@ Examples can serve as a starting template for customized usages.
     * __Features__: Cylinder, Sphere
     * [RodRigidBodyContact](./RigidBodyCases/RodRigidBodyContact)
       * __Purpose__: Demonstrate contact between cylinder and rod, for different intial conditions.
-      * __Features__: Cylinder, CosseratRods, ExternalContact
+      * __Features__: Cylinder, CosseratRods, RodCylinderContact
 * [HelicalBucklingCase](./HelicalBucklingCase)
     * __Purpose__: Demonstrate helical buckling with extreme twisting boundary condition.
     * __Features__: HelicalBucklingBC
 * [ContinuumFlagellaCase](./ContinuumFlagellaCase)
     * __Purpose__: Demonstrate flagella modeling using PyElastica.
     * __Features__: SlenderBodyTheory, MuscleTorques,
-    * [MuscularFlagella](./MuscularFlagella)
-        * __Purpose__: Example of customizing [Joint module](./MuscularFlagella/connection_flagella.py) and [Force module](./MuscularFlagella/muscle_forces_flagella.py) to implement muscular flagella.
-        * __Features__: MuscleForces(custom implemented)
+* [MuscularFlagella](./MuscularFlagella)
+    * __Purpose__: Example of customizing [Joint module](./MuscularFlagella/connection_flagella.py) and [Force module](./MuscularFlagella/muscle_forces_flagella.py) to implement muscular flagella.
+    * __Features__: MuscleForces(custom implemented)
 * [RodContactCase](./RodContactCase)
   * [RodRodContact](./RodContactCase/RodRodContact)
     * __Purpose__: Demonstrates contact between two rods, for different initial conditions.
-    * __Features__: CosseratRod, ExternalContact
+    * __Features__: CosseratRod, RodRodContact
   * [RodSelfContact](./RodContactCase/RodSelfContact)
     * [PlectonemesCase](./RodContactCase/RodSelfContact/PlectonemesCase)
       * __Purpose__: Demonstrates rod self contact with Plectoneme example, and how to use link-writhe-twist after simulation completed.
-      * __Features__: CosseratRod, SelonoidsBC, SelfContact, Link-Writhe-Twist
+      * __Features__: CosseratRod, SelonoidsBC, RodSelfContact, Link-Writhe-Twist
     * [SolenoidsCase](./RodContactCase/RodSelfContact/SolenoidsCase)
       * __Purpose__: Demonstrates rod self contact with Solenoid example, and how to use link-writhe-twist after simulation completed.
-      * __Features__: CosseratRod, SelonoidsBC, SelfContact, Link-Writhe-Twist
+      * __Features__: CosseratRod, SelonoidsBC, RodSelfContact, Link-Writhe-Twist
 * [BoundaryConditionsCases](./BoundaryConditionsCases)
     * __Purpose__: Demonstrate the usage of boundary conditions for constraining the movement of the system.
     * __Features__: GeneralConstraint, CosseratRod
@@ -75,6 +78,9 @@ Examples can serve as a starting template for customized usages.
 * [RingRodCase](./RingRodCase)
     * __Purpose__: Demonstrate simulation of ring rod.
     * __Features__: RingCosseratRod, OneEndFixedRod, GravityForce
+* [CatenaryCase](./CatenaryCase)
+    * __Purpose__: Demonstrate simulation of cosserat rod under gravity with fixed ends.
+    * __Features__: CosseratRod, FixedConstraint, GravityForce
 
 ## Functional Examples
 

From adbdb6c1c2ce5e16657e45fec800d828ae702ab4 Mon Sep 17 00:00:00 2001
From: Ali-7800 <47090295+Ali-7800@users.noreply.github.com>
Date: Thu, 22 Feb 2024 17:23:59 -0600
Subject: [PATCH 5/7] fix branch poetry

---
 poetry.lock    | 2066 ++++++++++++++++++++++++++++++++++++++++++++++++
 pyproject.toml |    2 +-
 2 files changed, 2067 insertions(+), 1 deletion(-)
 create mode 100644 poetry.lock

diff --git a/poetry.lock b/poetry.lock
new file mode 100644
index 00000000..8931e67e
--- /dev/null
+++ b/poetry.lock
@@ -0,0 +1,2066 @@
+# This file is automatically @generated by Poetry 1.5.1 and should not be changed by hand.
+
+[[package]]
+name = "accessible-pygments"
+version = "0.0.4"
+description = "A collection of accessible pygments styles"
+optional = true
+python-versions = "*"
+files = [
+    {file = "accessible-pygments-0.0.4.tar.gz", hash = "sha256:e7b57a9b15958e9601c7e9eb07a440c813283545a20973f2574a5f453d0e953e"},
+    {file = "accessible_pygments-0.0.4-py2.py3-none-any.whl", hash = "sha256:416c6d8c1ea1c5ad8701903a20fcedf953c6e720d64f33dc47bfb2d3f2fa4e8d"},
+]
+
+[package.dependencies]
+pygments = ">=1.5"
+
+[[package]]
+name = "alabaster"
+version = "0.7.13"
+description = "A configurable sidebar-enabled Sphinx theme"
+optional = true
+python-versions = ">=3.6"
+files = [
+    {file = "alabaster-0.7.13-py3-none-any.whl", hash = "sha256:1ee19aca801bbabb5ba3f5f258e4422dfa86f82f3e9cefb0859b283cdd7f62a3"},
+    {file = "alabaster-0.7.13.tar.gz", hash = "sha256:a27a4a084d5e690e16e01e03ad2b2e552c61a65469419b907243193de1a84ae2"},
+]
+
+[[package]]
+name = "autoflake8"
+version = "0.4.1"
+description = "Tool to automatically fix some issues reported by flake8 (forked from autoflake)."
+optional = false
+python-versions = ">=3.7,<4.0"
+files = [
+    {file = "autoflake8-0.4.1-py3-none-any.whl", hash = "sha256:fdf663b627993ac38e5b55b7d742c388fb2a4f34798a052f43eecc5e8d629e9d"},
+    {file = "autoflake8-0.4.1.tar.gz", hash = "sha256:c17da499bd2b71ba02fb11fe53ff1ad83d7dae6efb0f115fd1344f467797c679"},
+]
+
+[package.dependencies]
+pyflakes = ">=2.3.0"
+
+[[package]]
+name = "babel"
+version = "2.13.0"
+description = "Internationalization utilities"
+optional = true
+python-versions = ">=3.7"
+files = [
+    {file = "Babel-2.13.0-py3-none-any.whl", hash = "sha256:fbfcae1575ff78e26c7449136f1abbefc3c13ce542eeb13d43d50d8b047216ec"},
+    {file = "Babel-2.13.0.tar.gz", hash = "sha256:04c3e2d28d2b7681644508f836be388ae49e0cfe91465095340395b60d00f210"},
+]
+
+[package.dependencies]
+pytz = {version = ">=2015.7", markers = "python_version < \"3.9\""}
+
+[package.extras]
+dev = ["freezegun (>=1.0,<2.0)", "pytest (>=6.0)", "pytest-cov"]
+
+[[package]]
+name = "beautifulsoup4"
+version = "4.12.2"
+description = "Screen-scraping library"
+optional = true
+python-versions = ">=3.6.0"
+files = [
+    {file = "beautifulsoup4-4.12.2-py3-none-any.whl", hash = "sha256:bd2520ca0d9d7d12694a53d44ac482d181b4ec1888909b035a3dbf40d0f57d4a"},
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+]
+
+[package.dependencies]
+soupsieve = ">1.2"
+
+[package.extras]
+html5lib = ["html5lib"]
+lxml = ["lxml"]
+
+[[package]]
+name = "black"
+version = "21.12b0"
+description = "The uncompromising code formatter."
+optional = false
+python-versions = ">=3.6.2"
+files = [
+    {file = "black-21.12b0-py3-none-any.whl", hash = "sha256:a615e69ae185e08fdd73e4715e260e2479c861b5740057fde6e8b4e3b7dd589f"},
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+pathspec = ">=0.9.0,<1"
+platformdirs = ">=2"
+tomli = ">=0.2.6,<2.0.0"
+typing-extensions = [
+    {version = ">=3.10.0.0", markers = "python_version < \"3.10\""},
+    {version = ">=3.10.0.0,<3.10.0.1 || >3.10.0.1", markers = "python_version >= \"3.10\""},
+]
+
+[package.extras]
+colorama = ["colorama (>=0.4.3)"]
+d = ["aiohttp (>=3.7.4)"]
+jupyter = ["ipython (>=7.8.0)", "tokenize-rt (>=3.2.0)"]
+python2 = ["typed-ast (>=1.4.3)"]
+uvloop = ["uvloop (>=0.15.2)"]
+
+[[package]]
+name = "certifi"
+version = "2023.7.22"
+description = "Python package for providing Mozilla's CA Bundle."
+optional = false
+python-versions = ">=3.6"
+files = [
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+name = "cfgv"
+version = "3.4.0"
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+optional = false
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+files = [
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+description = "Backport of pathlib-compatible object wrapper for zip files"
+optional = false
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+testing = ["big-O", "jaraco.functools", "jaraco.itertools", "more-itertools", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-ignore-flaky", "pytest-mypy (>=0.9.1)", "pytest-ruff"]
+
+[extras]
+docs = ["Sphinx", "docutils", "myst-parser", "numpydoc", "readthedocs-sphinx-search", "sphinx-autodoc-typehints", "sphinx-book-theme"]
+examples = ["cma", "matplotlib"]
+
+[metadata]
+lock-version = "2.0"
+python-versions = ">=3.8,<3.12"
+content-hash = "c153b60e02556c520953aac32ee2d6260bbf4557c6d2202a47ded1995245413e"
diff --git a/pyproject.toml b/pyproject.toml
index 942fa5b2..4e5f998d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -46,7 +46,7 @@ tqdm = "^4.61.1"
 # below `extras`. They can be opted into by apps.
 Sphinx = {version = "^6.1", optional = true}
 sphinx-book-theme = {version = "^1.0", optional = true}
-readthedocs-sphinx-search = {version = ">=0.1.1,<0.4.0", optional = true}
+readthedocs-sphinx-search = {version = "^0.1.1", optional = true}
 sphinx-autodoc-typehints = {version = "^1.21", optional = true}
 myst-parser = {version = "^1.0", optional = true}
 numpydoc = {version = "^1.3.1", optional = true}

From 9698a3a933b0ca08de120e7e1e7961199c9e590a Mon Sep 17 00:00:00 2001
From: Ali-7800 <47090295+Ali-7800@users.noreply.github.com>
Date: Fri, 23 Feb 2024 13:56:39 -0600
Subject: [PATCH 6/7] citation for catenary solution added

---
 examples/CatenaryCase/post_processing.py | 4 +++-
 examples/README.md                       | 2 +-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/examples/CatenaryCase/post_processing.py b/examples/CatenaryCase/post_processing.py
index 9b695fca..ba6af0e3 100644
--- a/examples/CatenaryCase/post_processing.py
+++ b/examples/CatenaryCase/post_processing.py
@@ -44,9 +44,11 @@ def plot_video(
 
 
 def plot_catenary(plot_params: dict, xlim=(0, 1), ylim=(-0.5, 0.5), base_length=1.0):
+    """
+    Catenary analytical solution from Routh, Edward John (1891). "Chapter X: On Strings". A Treatise on Analytical Statics. University Press.
+    """
     matplotlib.use("TkAgg")
     position = np.array(plot_params["position"])
-    n_elem = position.shape[-1]
     lowest_point = np.min(position[-1][2])
     x_catenary = np.linspace(0, base_length, 100)
 
diff --git a/examples/README.md b/examples/README.md
index 39f6ddce..961f7618 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -79,7 +79,7 @@ Examples can serve as a starting template for customized usages.
     * __Purpose__: Demonstrate simulation of ring rod.
     * __Features__: RingCosseratRod, OneEndFixedRod, GravityForce
 * [CatenaryCase](./CatenaryCase)
-    * __Purpose__: Demonstrate simulation of cosserat rod under gravity with fixed ends.
+    * __Purpose__: Demonstrate simulation of cosserat rod under gravity with fixed ends, compared with Catenary Analytical Solution from Routh, Edward John (1891). [<strong>"Chapter X: On Strings".</strong>](https://books.google.com/books?id=3N5JAAAAMAAJ&pg=PA315#v=onepage&q&f=false). A Treatise on Analytical Statics. University Press.
     * __Features__: CosseratRod, FixedConstraint, GravityForce
 
 ## Functional Examples

From 76e6afae0b83c9fc10cfb215b5727ad4f54203ea Mon Sep 17 00:00:00 2001
From: Ali-7800 <47090295+Ali-7800@users.noreply.github.com>
Date: Fri, 23 Feb 2024 13:58:24 -0600
Subject: [PATCH 7/7] formatting

---
 examples/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/examples/README.md b/examples/README.md
index 961f7618..06f214be 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -79,7 +79,7 @@ Examples can serve as a starting template for customized usages.
     * __Purpose__: Demonstrate simulation of ring rod.
     * __Features__: RingCosseratRod, OneEndFixedRod, GravityForce
 * [CatenaryCase](./CatenaryCase)
-    * __Purpose__: Demonstrate simulation of cosserat rod under gravity with fixed ends, compared with Catenary Analytical Solution from Routh, Edward John (1891). [<strong>"Chapter X: On Strings".</strong>](https://books.google.com/books?id=3N5JAAAAMAAJ&pg=PA315#v=onepage&q&f=false). A Treatise on Analytical Statics. University Press.
+    * __Purpose__: Demonstrate simulation of cosserat rod under gravity with fixed ends, compared with Catenary Analytical Solution from Routh, Edward John (1891). [<strong>"Chapter X: On Strings"</strong>](https://books.google.com/books?id=3N5JAAAAMAAJ&pg=PA315#v=onepage&q&f=false). A Treatise on Analytical Statics. University Press.
     * __Features__: CosseratRod, FixedConstraint, GravityForce
 
 ## Functional Examples