Propositional logic deals with simple statements that are either true or false. It uses logical connectives to build complex expressions. Example: P ^ Q if both P and Q are true, then the whole expression is true. Propositions Proof Theory focuses on the rules for logical deductions and includes completeness,Continue Reading
An invertible matrix must be a square matrix: The formula is: B = A−1 Non-square matrices (m-by-n matrices for which m ≠ n}}) do not have an inverse, but can in sometimes have a left inverse or right inverse.Continue Reading
The friction force is the force exerted by a surface when an object exerts force across it. A coefficient of friction(μ) is a scalar proportion of two objects and their normal reaction. There are 2 cases: Is the dynamic/kinetic coefficient of friction when either or both objects are dynamic. IsContinue Reading
The relationship between body, forces acting upon it, and its motion. In an inertial frame of reference is when net force is equal to zero = therefore there is no resistance to the object’s velocity. First law: In an inertial frame of reference, an object either remains at rest orContinue Reading
Property P(n) holds for every natural number n(0….N) or every between (x∈N…N) The method of induction requires two cases to be proved. The base case (or, sometimes, the basis), proves that the property holds for the number 0. (This is easy to compute and check for the number n). TheContinue Reading
Pseudo code with arbitrary values of a Simple Bicycle Model given steering change. The x-axis points to the forward direction or the longitudinal direction The y-axis, which represents the lateral direction is positive when it points to the right of the driver The z-axis points to the ground satisfying theContinue Reading
Is a force(tension force to be exact) that makes a body follow a curved path with a center. The force’s direction is always to the instantaneous center of the path and orthogonal to the motion of the body. The body’s acceleration can be calculated as: a= v^2/r (where v squaredContinue Reading
Unbalanced forces create acceleration in the direction of the Net force. Fy = my” Which is the translational acceleration in the y direction Unbalanced moments create acceleration in the direction of the Net moment/torque around a given axis, where α is the angular acceleration(rad/sec*sec),I – moment of Inertia(3X3). τ =Continue Reading
When a rotor spins it produces thrust(F) and also induces moment(M)(torque) both are measured by radians/sec with omega(ω). The moment induced is in the counter direction(A.K.A yaw – which is rotation around the Z value) when ω is 2*PI the rotor is doing 1 full rotation per second. The formulasContinue Reading
Four possible perspectives(ways) to produce matrix multiplications(which give the same result): Ordered Collection of Dot Products (result matrix is built elementwise): Left matrix is rows, right matrix is columns. Each element is the dot product of a corresponding row from the left matrix and the column from the right matrix.Continue Reading