Mechanics of Marine Machines 2 min read
Grashof’s Law
The Grashof’s law states that for a four-bar linkage system, the sum of the shortest and longest link of a…
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Mechanics of Marine Machines 3 min read
Kinematic Inversions of Four Bar Chain
Inversions of mechanism: A mechanism is one in which one of the links of a kinematic chain is fixed. Different mechanisms…
Mechanics of Marine Machines 2 min read
Kinematic Inversion
Every mechanism has moving members which move relative to each other about the joints connecting them. These relative motions result…
Mathematics for Marine Engineering 2 min read
Methods of Integration
Integration is not as easy as differentiation. This is first due to its nature. Finding a derivative of a given…
Mathematics for Marine Engineering 1 min read
Cartesian Coordinates
Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is: They are also called Rectangular Coordinates because it…
Mathematics for Marine Engineering 3 min read
Integral Calculus
Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus in the mid-17th century. Leibnitz, a German philosopher, mathematician, and…
Mathematics for Marine Engineering 2 min read
Lagrange Multipliers
In the previous section we optimized (i.e. found the absolute extrema) a function on a region that contained its boundary. Finding…
Mathematics for Marine Engineering 2 min read
Finding Maxima and Minima using Derivatives
Where is a function at a high or low point? Calculus can help! A maximum is a high point and…
Mathematics for Marine Engineering 1 min read
Examples on Chain Rule (Differentiation Rules)
Examples on Chain Rule Example 10.8 Find F′(x) if F (x) = √[x2 +1] Solution Take u = g(x) = x2 + 1 and f (u) =√u ∴ F (x) = ( fog)(x) = f (g(x)) Example 10.9 Differentiate…
Mathematics for Marine Engineering 1 min read
Euler’s Homogeneous Function Theorem
Let be a homogeneous function of order so that (1) Then define and . Then (2) (3) (4) Let , then (5) This can be generalized to…
Mathematics for Marine Engineering 3 min read
Homogeneous Functions
To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y) In other words Homogeneous is when we can take a function:f(x,y)…