From f83905fc05c56c74cca0d87b965f35807ccbef4b Mon Sep 17 00:00:00 2001 From: agyao2 Date: Sat, 7 Feb 2026 17:20:52 -0600 Subject: [PATCH 1/5] Coordinate systems additions Adds 2D and 3D subsections and puts existing subsections within them and adds position, velocity, acceleration equations for cartesian and polar --- src/pages/dyn/coordinate_systems.astro | 48 +++++++++++++++++--------- 1 file changed, 32 insertions(+), 16 deletions(-) diff --git a/src/pages/dyn/coordinate_systems.astro b/src/pages/dyn/coordinate_systems.astro index 6c1fa8186..6356d74a1 100644 --- a/src/pages/dyn/coordinate_systems.astro +++ b/src/pages/dyn/coordinate_systems.astro @@ -23,18 +23,28 @@ import InlineCanvas from "../../components/InlineCanvas.astro" --- -
+
+
  • 2D + +
  • +
  • 3D + +
  • +
    - + + +

    Cartesian coordinates (also known as rectangular @@ -79,7 +89,9 @@ import InlineCanvas from "../../components/InlineCanvas.astro"

    - +

    @@ -114,9 +126,9 @@ import InlineCanvas from "../../components/InlineCanvas.astro"

    -
    + - +

    Polar coordinates are an alternative 2D coordinate system @@ -171,7 +183,9 @@ import InlineCanvas from "../../components/InlineCanvas.astro"

    - +

    @@ -224,9 +238,11 @@ import InlineCanvas from "../../components/InlineCanvas.astro"

    -
    + + + - +

    The spherical coordinate system extends polar coordinates @@ -491,9 +507,9 @@ import InlineCanvas from "../../components/InlineCanvas.astro"

    -
    + - +

    The cylindrical coordinate system extends polar coordinates into 3D by using the standard vertical coordinate \(z\) for the third. @@ -698,7 +714,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro" vector derivatives.

    -
    + From 01f234335a026f645d5ed5fe3cd1cb238cce5ee2 Mon Sep 17 00:00:00 2001 From: agyao2 Date: Sat, 7 Feb 2026 17:47:11 -0600 Subject: [PATCH 2/5] Rotation of arbitrary reference points move Moves rotation of arbitrary reference points to momentum page --- src/pages/dyn/momentum.astro | 57 ++++++++++++++++++++++++- src/pages/dyn/rigid_body_kinetics.astro | 51 ---------------------- 2 files changed, 56 insertions(+), 52 deletions(-) diff --git a/src/pages/dyn/momentum.astro b/src/pages/dyn/momentum.astro index e6533c41a..eceb0c709 100644 --- a/src/pages/dyn/momentum.astro +++ b/src/pages/dyn/momentum.astro @@ -30,6 +30,7 @@ import Col from "../../components/Col.astro"
  • Momentum
  • Impulse
  • Collisions
  • +
  • Rotation about arbitrary reference points
  • @@ -675,7 +676,61 @@ import Col from "../../components/Col.astro" - + +

    + In some cases, using the center of mass as a reference point is not ideal, and we might encounter situations in which we would need to consider the dynamics about another point. + We will begin by finding the angular momentum of a rigid body about any arbitrary point, and extend that from there. +

    + +

    + We can differentiate the above expression with respect to time and obtain the time derivative of the angular momentum of the rigid body about point \(P\). + This will yield two important special cases of rotations. +

    + +

    + The important special cases are outlined below. +

    + + + + + case + + + result + + + consequence + + + + + + + \(P = C\) + + + + + + This is Euler's 2nd law. + + + + + + + + + + + The rigid body is rotating about a fixed point \(P\). + This is another form of Euler's 2nd law. + + + + +
    diff --git a/src/pages/dyn/rigid_body_kinetics.astro b/src/pages/dyn/rigid_body_kinetics.astro index 2f1fbc533..000885e89 100644 --- a/src/pages/dyn/rigid_body_kinetics.astro +++ b/src/pages/dyn/rigid_body_kinetics.astro @@ -29,8 +29,6 @@ import Row from "../../components/Row.astro" @@ -102,55 +100,6 @@ import Row from "../../components/Row.astro" - - -

    - In some cases, using the center of mass as a reference point is not ideal, and we might encounter - situations in which we would need to consider the dynamics about another point. We will begin by - finding the angular momentum of a rigid body about any arbitrary point, and extend that from there. -

    - - - -

    - We can differentiate the above expression with respect to time and obtain the time derivative of - the angular momentum of the rigid body about point \(P\). This will yield two important special cases of - rotations. -

    - - - -

    - The important special cases are outlined below. -

    - - - - - case - result - consequence - - - - - \(P = C\) - - This is Euler's 2nd law. - - - - - - - The rigid body is rotating about a fixed point \(P\). This is another - form of Euler's 2nd law. - - - - -
    - From 05c3fefb3c00628bb99e02b73ee69b17753257a8 Mon Sep 17 00:00:00 2001 From: agyao2 Date: Sat, 7 Feb 2026 18:06:04 -0600 Subject: [PATCH 3/5] MBS updates Makes chains into its own subsubsection and adds it to the navbar and comments out standard sign convention subsubsection --- .../multi_body_systems/GearsChains_edited.png | Bin 49379 -> 40865 bytes src/pages/dyn/multi_body_systems.astro | 13 ++++++++----- 2 files changed, 8 insertions(+), 5 deletions(-) diff --git a/public/dyn/multi_body_systems/GearsChains_edited.png b/public/dyn/multi_body_systems/GearsChains_edited.png index 719d4edfe68035e127ef36c441568c070e63288b..215303eb8fe2f86a075944498f181c4fa62feaa5 100644 GIT binary patch literal 40865 zcmaHTWmuG36z(X}(k0y;3P|^$ba$gjcQYUgVHITf&x;~-3<~F10oG~3&bPm{*Iw&g?|PSEYAUi=7-Sd_2n0)B?u7;ff)oLPJn%w$2wn+plMett z9=K`9LLn7H6g%LTM^;kGQV>X0H0JedWbiw>vz)#g1cKdl|NnzTc5HG8B%5FUg_IV| zWPj01PjmVX^(ffzJ#J2g!J~IY9)SqK#By 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    • Gears - - - - -

      @@ -73,6 +69,12 @@ import DisplayTable from "../../components/DisplayTable.astro" + + + + + + From d29e060d404630a6fb9851af6b0234ccc538900c Mon Sep 17 00:00:00 2001 From: agyao2 Date: Sat, 7 Feb 2026 19:07:36 -0600 Subject: [PATCH 4/5] Gear kinetics Commented out gear kinetics --- src/pages/dyn/multi_body_systems.astro | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/pages/dyn/multi_body_systems.astro b/src/pages/dyn/multi_body_systems.astro index 281c7aaa7..00c7c33d7 100644 --- a/src/pages/dyn/multi_body_systems.astro +++ b/src/pages/dyn/multi_body_systems.astro @@ -112,6 +112,7 @@ import DisplayTable from "../../components/DisplayTable.astro" + Image from Wikimedia. CC BY 2.0 From 49a1d142a4957ade9d2651bcc66908805b2b85b9 Mon Sep 17 00:00:00 2001 From: agyao2 Date: Sat, 7 Feb 2026 20:53:46 -0600 Subject: [PATCH 5/5] Rigid body kinetics solution steps Adds recommended solution steps to rigid body kinetics page --- src/pages/dyn/rigid_body_kinetics.astro | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/src/pages/dyn/rigid_body_kinetics.astro b/src/pages/dyn/rigid_body_kinetics.astro index 000885e89..a5de96515 100644 --- a/src/pages/dyn/rigid_body_kinetics.astro +++ b/src/pages/dyn/rigid_body_kinetics.astro @@ -101,5 +101,14 @@ import Row from "../../components/Row.astro" + + The steps involved in analyzing a rigid body mechanical system with Newton's equations are as follows. + + +