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Calculating
Published in Victor A. Bloomfield, Using R for Numerical Analysis in Science and Engineering, 2018
R can be used, without any programming, as a powerful calculator. It has all the standard arithmetic operators and functions, which operate on numeric or complex vectors (including scalars, which are vectors of length 1). Arithmetic operators: The binary arithmetic operators are +, -, *, /, ^ (exponentiation), %% (mod), and %/% (integer division).Logarithms and exponentials: log (natural log), log10, (base 10 log), log2 (base 2 log), log (x,b) (log of x to base b). log1p(x) computes log(1+x) accurately for |x| << 1.exp computes the exponential function, and expm1 computes exp(x)-1 accurately for |x| << 1.Trigonometric functions : cos(x), sin(x), tan(x), acos(x), asin(x), atan(x), atan2(y,x) where angles are in radians and x and y are numeric or complex scalars or vectors. atan2(y,x) = atan(y/x) for positive arguments. The pracma package, to which we will refer later, adds more trigonometric functions: cot(x), csc(x), sec(x), acot(x), acsc(x), asec(x).Hyperbolic functions : cosh(x), sinh(x), tanh(x), acosh(x), asinh(x), atanh(x). pracma adds coth(x), csch(x), sech(x), acoth(x), acsch(x), asech(x).Miscellaneous mathematical functions: abs(x), sqrt(x).
Evaluation of maximum thigh angular acceleration during the swing phase of steady-speed running
Published in Sports Biomechanics, 2023
Kenneth P. Clark, Laurence J. Ryan, Christopher R. Meng, David J. Stearne
All angles in the model equations are measured in radians referenced to a vertical axis perpendicular to the ground. Experimentally measured angles in degrees can be expressed in radians by the standard conversion factor (2π rad/360 deg). The thigh segment moves from a positive maximum angle at peak flexion to zero at the downward vertical position to a negative maximum angle at peak extension. The total thigh range of motion (θtotal) is determined from peak extension to peak flexion of the thigh segment. The phase value (θphase) allows the experimental data acquisition of the thigh segment to occur at any time during the rotation cycle and determines the temporal position of the model equations on θ(t) vs. t, ω(t) vs. t and α(t) vs. t graphs. The offset angle (θshift) determines the central angular position of the sine wave model equation on the θ(t) vs. t graph. Conceptually, the θshift value represents a single metric to quantify the extent to which the mean thigh angular motion, averaged over the entire stride cycle, occurs in front or behind the vertical axis. From a practical standpoint, this θshift value is related to how ‘front-side’ thigh mechanics are shifted (Haugen et al., 2018; Kratky et al., 2016; R. V. Mann & Murphy, 2018).