Started the physics engine

Started a physical system class together with Body and Force

Author: jCodingStuff

manimlib/physics/__init__.py

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+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    import numpy as np
+    from manimlib.mobject.mobject import Mobject
+
+
+class Body:
+    """
+    Represents a body in a physical system
+    """
+
+    def __init__(
+        self,
+        mass: float,
+        pos: np.ndarray,
+        mobj: Mobject
+    ) -> None:
+        """
+        Initialize a new Body object
+        """
+
+        self.mass: float = mass
+        if self.mass < 0:
+            raise Exception(
+                f"Current value for mass ({self.mass}) is negative!"
+            )
+        
+        self.pos: np.ndarray = pos
+        if len(self.pos.shape) != 1 or self.pos.shape[0] == 3:
+            raise Exception("Position is invalid!")
+        
+        self.mobj: Mobject = mobj
+        self.mobj.move_to(self.pos)
+
+        # index of the body in the physical system, to be set
+        # by a PhysicalSystem
+        self.index: int = -1

manimlib/physics/body.py

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+from abc import ABCMeta, abstractmethod
+
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    import numpy as np
+    from manimlib.physics.body import Body
+
+
+
+class Force(metaclass=ABCMeta):
+    """
+    Represents a force among bodies in a physical
+    system
+    """
+
+    def __init__(self, bodies: tuple[Body]) -> None:
+        """
+        Initialize a new Force object
+
+        Keyword arguments
+        -----------------
+        bodies: the bodies to which the force applies
+        """
+        self.bodies: tuple[Body] = bodies
+        if not self.bodies:
+            raise Exception("No bodies have been provided!")
+    
+    @abstractmethod
+    def apply(forces: np.ndarray):
+        """
+        Apply the force and add the contributions to the 'total'
+        forces in the system
+
+        Keyword arguments
+        -----------------
+        forces: with shape (nbodies, DIMENSIONS), each row stores the
+                total force exerted in the body with that index
+        """
+        pass
+
+
+class NewtonGravitationalForce(Force):
+    """
+    Newton's gravitational force between two masses
+    F = - G * m1 * m2 / r^2
+    """
+
+    def __init__(self, bodies: tuple[Body]) -> None:
+        super().__init__(bodies)

manimlib/physics/force.py

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+from manimlib.mobject.mobject import Mobject
+
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from manimlib.physics.body import Body
+    from manimlib.physics.force import Force
+
+class PhysicalSystem(Mobject):
+    """
+    Represents a physical system
+    """
+
+    def __init__(self, bodies: list[Body]=[], forces: list[Force]=[], **kwargs):
+        super().__init__(**kwargs)
+        self.bodies: list[Body] = bodies
+        for i, body in enumerate(self.bodies):  # set indices for the bodies
+            body.index = i
+        self.forces: list[Force] = forces