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A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions. Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg , where F is the force exerted on a mass m by the Earth's gravitational field of strength g .
Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).
As shown above in the Displacement section, the horizontal and vertical velocity of a projectile are independent of each other. Because of this, we can find the time to reach a target using the displacement formula for the horizontal velocity:
A truss element can only transmit forces in compression or tension. This means that in two dimensions, each node has two degrees of freedom (DOF): horizontal and vertical displacement. The resulting equation contains a four by four stiffness matrix.
For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. When there are degrees of freedom a matrix must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
In this case, the equation governing the beam's deflection can be approximated as: = () where the second derivative of its deflected shape with respect to (being the horizontal position along the length of the beam) is interpreted as its curvature, is the Young's modulus, is the area moment of inertia of the cross-section, and is the internal ...
They then calculate the righting moment at this angle, which is determined using the equation: = Where RM is the righting moment, GZ is the righting arm and Δ is the displacement. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel.