Formulas: Drive (Output) Transformation Derivation · MIL-STD-810H

Formula 1

(3) Substituting results from (2) yields

\mathbf{F} \equiv \underset{N_{s} \mathrm{x} 1}{\mathbf{P}^{T}} \underset{N_{s} \mathrm{x} 6}{\mathbf{D}}=\underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\left[\begin{array}{cc}\underset{6 \mathrm{x} N_{s}}{\mathbf{P}} & \underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\end{array}\right] \underset{6 \mathrm{x} 1}{\mathbf{C}}

\mathbf{F} \equiv \underset{N_{s} \mathrm{x} 1}{\mathbf{P}^{T}} \underset{N_{s} \mathrm{x} 6}{\mathbf{D}}=\underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\left[\begin{array}{cc}\underset{6 \mathrm{x} N_{s}}{\mathbf{P}} & \underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\end{array}\right] \underset{6 \mathrm{x} 1}{\mathbf{C}}

Formula 2

d. The discussions within this paragraph and previous derivation assumed Nd = 6. In the event Nd <6, Nd would represent the actual number of mechanical DOFs. In terms of the nomenclature of Figure 2, and assuming matched actuators are employed, voltage drives to the shakers for the over-actuated scenario would be defined as Equation 4.5:

\{\mathbf{s}\}=\mathbf{T}_{\mathrm{s}}\{\mathbf{d}\}

Formula 1

(3) Substituting results from (2) yields

\mathbf{F} \equiv \underset{N_{s} \mathrm{x} 1}{\mathbf{P}^{T}} \underset{N_{s} \mathrm{x} 6}{\mathbf{D}}=\underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\left[\begin{array}{cc}\underset{6 \mathrm{x} N_{s}}{\mathbf{P}} & \underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\end{array}\right] \underset{6 \mathrm{x} 1}{\mathbf{C}}

\mathbf{F} \equiv \underset{N_{s} \mathrm{x} 1}{\mathbf{P}^{T}} \underset{N_{s} \mathrm{x} 6}{\mathbf{D}}=\underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\left[\begin{array}{cc}\underset{6 \mathrm{x} N_{s}}{\mathbf{P}} & \underset{N_{s} \mathrm{x} 6}{\mathbf{P}^{T}}\end{array}\right] \underset{6 \mathrm{x} 1}{\mathbf{C}}

Formula 2

\{\mathbf{s}\}=\mathbf{T}_{\mathrm{s}}\{\mathbf{d}\}