using matlab to simplify calculation
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%%%simplify.msyms nc_x nc_y nc_z diffPos_x diffPos_y diffPos_z vc_x vc_y vc_z ... nw_x nw_y nw_z real;d_Rsd_T = [nc_x * diffPos_x + vc_x * nw_x ... nc_y * diffPos_x + vc_y * nw_x ... nc_z * diffPos_x + vc_z * nw_x ... nc_x * diffPos_y + vc_x * nw_y ... nc_y * diffPos_y + vc_y * nw_y ... nc_z * diffPos_y + vc_z * nw_y ... nc_x * diffPos_z + vc_x * nw_z ... nc_y * diffPos_z + vc_y * nw_z ... nc_z * diffPos_z + vc_z * nw_z ... nw_x ... nw_y ... nw_z ];syms dqb_q0_x dqb_q0_y dqb_q0_z dqb_q0_w ... dqb_qe_x dqb_qe_y dqb_qe_z dqb_qe_w real;d_T_BDQ = [ 0 0 -2*dqb_q0_y -2*dqb_q0_z 0 0 0 0; -dqb_q0_z dqb_q0_y dqb_q0_x -dqb_q0_w 0 0 0 0; dqb_q0_y dqb_q0_z dqb_q0_w dqb_q0_x 0 0 0 0; dqb_q0_z dqb_q0_y dqb_q0_x dqb_q0_w 0 0 0 0; 0 -2*dqb_q0_x 0 -2*dqb_q0_z 0 0 0 0; -dqb_q0_x -dqb_q0_w dqb_q0_z dqb_q0_y 0 0 0 0; -dqb_q0_y dqb_q0_z -dqb_q0_w dqb_q0_x 0 0 0 0; dqb_q0_x dqb_q0_w dqb_q0_z dqb_q0_y 0 0 0 0; 0 -2*dqb_q0_x -2*dqb_q0_y 0 0 0 0 0; dqb_qe_x -dqb_qe_w dqb_qe_z -dqb_qe_y -dqb_q0_x dqb_q0_w -dqb_q0_z dqb_q0_y; dqb_qe_y -dqb_qe_z -dqb_qe_w dqb_qe_x -dqb_q0_y dqb_q0_z dqb_q0_w -dqb_q0_x; dqb_qe_z dqb_qe_y -dqb_qe_x -dqb_qe_w -dqb_q0_z -dqb_q0_y dqb_q0_x dqb_q0_w; ];syms dqn_q0_x dqn_q0_y dqn_q0_z dqn_q0_w dqn_qe_x dqn_qe_y dqn_qe_z dqn_qe_w nw_x_a0 nw_x_ae; d_BDQ_se3 = [ -dqn_q0_x * nw_x_a0, -dqn_q0_y * nw_x_a0, -dqn_q0_z * nw_x_a0, 0, 0, 0; dqn_q0_w * nw_x_a0, dqn_q0_z * nw_x_a0, -dqn_q0_y * nw_x_a0, 0, 0, 0; -dqn_q0_z * nw_x_a0, dqn_q0_w * nw_x_a0, dqn_q0_x * nw_x_a0, 0, 0, 0; dqn_q0_y * nw_x_a0, -dqn_q0_x * nw_x_a0, dqn_q0_w * nw_x_a0, 0, 0, 0; -dqn_q0_x * nw_x_ae - dqn_qe_x * nw_x_a0, -dqn_q0_y * nw_x_ae - dqn_qe_y * nw_x_a0,... -dqn_q0_z * nw_x_ae - dqn_qe_z * nw_x_a0, -dqn_q0_x * nw_x_a0,... -dqn_q0_y * nw_x_a0, -dqn_q0_z * nw_x_a0; dqn_q0_w * nw_x_ae + dqn_qe_w * nw_x_a0, dqn_q0_z * nw_x_ae + dqn_qe_z * nw_x_a0,... -dqn_q0_y * nw_x_ae - dqn_qe_y * nw_x_a0, dqn_q0_w * nw_x_a0,... dqn_q0_z * nw_x_a0, -dqn_q0_y * nw_x_a0; -dqn_q0_z * nw_x_ae - dqn_qe_z * nw_x_a0, dqn_q0_w * nw_x_ae + dqn_qe_w * nw_x_a0,... dqn_q0_x * nw_x_ae + dqn_qe_x * nw_x_a0,-dqn_q0_z * nw_x_a0,... . dqn_q0_w * nw_x_a0, dqn_q0_x * nw_x_a0; dqn_q0_y * nw_x_ae + dqn_qe_y * nw_x_a0, -dqn_q0_x * nw_x_ae - dqn_qe_x *nw_x_a0,... dqn_q0_w * nw_x_ae + dqn_qe_w * nw_x_a0, dqn_q0_y * nw_x_a0,... -dqn_q0_x * nw_x_a0, dqn_q0_w * nw_x_a0 ];d_Rsd_se3 = d_Rsd_T * d_T_BDQ * d_BDQ_se3;
%process_string.mresult = {'(dqn_q0_w*nw_x_ae + dqn_qe_w*nw_x_a0)*(dqb_q0_w*nw_x - dqb_q0_y*nw_z + dqb_q0_z*nw_y) + (dqn_q0_x*nw_x_ae + dqn_qe_x*nw_x_a0)*(dqb_q0_x*nw_x + dqb_q0_y*nw_y + dqb_q0_z*nw_z) + (dqn_q0_y*nw_x_ae + dqn_qe_y*nw_x_a0)*(dqb_q0_w*nw_z - dqb_q0_x*nw_y + dqb_q0_y*nw_x) - (dqn_q0_z*nw_x_ae + dqn_qe_z*nw_x_a0)*(dqb_q0_w*nw_y + dqb_q0_x*nw_z - dqb_q0_z*nw_x) - dqn_q0_x*nw_x_a0*(dqb_qe_x*nw_x + dqb_qe_y*nw_y + dqb_qe_z*nw_z - dqb_q0_z*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_z*(diffPos_y*nc_x + nw_y*vc_x) + dqb_q0_y*(diffPos_x*nc_z + nw_x*vc_z) - dqb_q0_y*(diffPos_z*nc_x + nw_z*vc_x) - dqb_q0_x*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_x*(diffPos_z*nc_y + nw_z*vc_y)) + dqn_q0_y*nw_x_a0*(dqb_qe_x*nw_y - dqb_qe_w*nw_z - dqb_qe_y*nw_x - dqb_q0_w*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_w*(diffPos_y*nc_x + nw_y*vc_x) - 2*dqb_q0_z*(diffPos_x*nc_x + nw_x*vc_x) + dqb_q0_x*(diffPos_x*nc_z + nw_x*vc_z) + dqb_q0_x*(diffPos_z*nc_x + nw_z*vc_x) - 2*dqb_q0_z*(diffPos_y*nc_y + nw_y*vc_y) + dqb_q0_y*(diffPos_y*nc_z + nw_\\\ny*vc_z) + dqb_q0_y*(diffPos_z*nc_y + nw_z*vc_y)) - dqn_q0_z*nw_x_a0*(dqb_qe_z*nw_x - dqb_qe_x*nw_z - dqb_qe_w*nw_y - 2*dqb_q0_y*(diffPos_x*nc_x + nw_x*vc_x) + dqb_q0_x*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_x*(diffPos_y*nc_x + nw_y*vc_x) + dqb_q0_w*(diffPos_x*nc_z + nw_x*vc_z) - dqb_q0_w*(diffPos_z*nc_x + nw_z*vc_x) + dqb_q0_z*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_z*(diffPos_z*nc_y + nw_z*vc_y) - 2*dqb_q0_y*(diffPos_z*nc_z + nw_z*vc_z)) + dqn_q0_w*nw_x_a0*(dqb_qe_y*nw_z - dqb_qe_w*nw_x - dqb_qe_z*nw_y + dqb_q0_y*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_y*(diffPos_y*nc_x + nw_y*vc_x) - 2*dqb_q0_x*(diffPos_y*nc_y + nw_y*vc_y) - dqb_q0_w*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_w*(diffPos_z*nc_y + nw_z*vc_y) + dqb_q0_z*(diffPos_x*nc_z + nw_x*vc_z) + dqb_q0_z*(diffPos_z*nc_x + nw_z*vc_x) - 2*dqb_q0_x*(diffPos_z*nc_z + nw_z*vc_z))'; '(dqn_q0_w*nw_x_ae + dqn_qe_w*nw_x_a0)*(dqb_q0_w*nw_y + dqb_q0_x*nw_z - dqb_q0_z*nw_x) - (dqn_q0_x*nw_x_ae + dqn_qe_x*nw_x_a0)*(dqb_q0_w*nw_z - dqb_q0_x*nw_y + dqb_q0_y*nw_x) + (dqn_q0_y*nw_x_ae + dqn_qe_y*nw_x_a0)*(dqb_q0_x*nw_x + dqb_q0_y*nw_y + dqb_q0_z*nw_z) + (dqn_q0_z*nw_x_ae + dqn_qe_z*nw_x_a0)*(dqb_q0_w*nw_x - dqb_q0_y*nw_z + dqb_q0_z*nw_y) - dqn_q0_y*nw_x_a0*(dqb_qe_x*nw_x + dqb_qe_y*nw_y + dqb_qe_z*nw_z - dqb_q0_z*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_z*(diffPos_y*nc_x + nw_y*vc_x) + dqb_q0_y*(diffPos_x*nc_z + nw_x*vc_z) - dqb_q0_y*(diffPos_z*nc_x + nw_z*vc_x) - dqb_q0_x*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_x*(diffPos_z*nc_y + nw_z*vc_y)) - dqn_q0_x*nw_x_a0*(dqb_qe_x*nw_y - dqb_qe_w*nw_z - dqb_qe_y*nw_x - dqb_q0_w*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_w*(diffPos_y*nc_x + nw_y*vc_x) - 2*dqb_q0_z*(diffPos_x*nc_x + nw_x*vc_x) + dqb_q0_x*(diffPos_x*nc_z + nw_x*vc_z) + dqb_q0_x*(diffPos_z*nc_x + nw_z*vc_x) - 2*dqb_q0_z*(diffPos_y*nc_y + nw_y*vc_y) + dqb_q0_y*(diffPos_y*nc_z + nw_\\\ny*vc_z) + dqb_q0_y*(diffPos_z*nc_y + nw_z*vc_y)) + dqn_q0_w*nw_x_a0*(dqb_qe_z*nw_x - dqb_qe_x*nw_z - dqb_qe_w*nw_y - 2*dqb_q0_y*(diffPos_x*nc_x + nw_x*vc_x) + dqb_q0_x*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_x*(diffPos_y*nc_x + nw_y*vc_x) + dqb_q0_w*(diffPos_x*nc_z + nw_x*vc_z) - dqb_q0_w*(diffPos_z*nc_x + nw_z*vc_x) + dqb_q0_z*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_z*(diffPos_z*nc_y + nw_z*vc_y) - 2*dqb_q0_y*(diffPos_z*nc_z + nw_z*vc_z)) + dqn_q0_z*nw_x_a0*(dqb_qe_y*nw_z - dqb_qe_w*nw_x - dqb_qe_z*nw_y + dqb_q0_y*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_y*(diffPos_y*nc_x + nw_y*vc_x) - 2*dqb_q0_x*(diffPos_y*nc_y + nw_y*vc_y) - dqb_q0_w*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_w*(diffPos_z*nc_y + nw_z*vc_y) + dqb_q0_z*(diffPos_x*nc_z + nw_x*vc_z) + dqb_q0_z*(diffPos_z*nc_x + nw_z*vc_x) - 2*dqb_q0_x*(diffPos_z*nc_z + nw_z*vc_z))'; '(dqn_q0_w*nw_x_ae + dqn_qe_w*nw_x_a0)*(dqb_q0_w*nw_z - dqb_q0_x*nw_y + dqb_q0_y*nw_x) + (dqn_q0_x*nw_x_ae + dqn_qe_x*nw_x_a0)*(dqb_q0_w*nw_y + dqb_q0_x*nw_z - dqb_q0_z*nw_x) - (dqn_q0_y*nw_x_ae + dqn_qe_y*nw_x_a0)*(dqb_q0_w*nw_x - dqb_q0_y*nw_z + dqb_q0_z*nw_y) + (dqn_q0_z*nw_x_ae + dqn_qe_z*nw_x_a0)*(dqb_q0_x*nw_x + dqb_q0_y*nw_y + dqb_q0_z*nw_z) - dqn_q0_z*nw_x_a0*(dqb_qe_x*nw_x + dqb_qe_y*nw_y + dqb_qe_z*nw_z - dqb_q0_z*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_z*(diffPos_y*nc_x + nw_y*vc_x) + dqb_q0_y*(diffPos_x*nc_z + nw_x*vc_z) - dqb_q0_y*(diffPos_z*nc_x + nw_z*vc_x) - dqb_q0_x*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_x*(diffPos_z*nc_y + nw_z*vc_y)) + dqn_q0_w*nw_x_a0*(dqb_qe_x*nw_y - dqb_qe_w*nw_z - dqb_qe_y*nw_x - dqb_q0_w*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_w*(diffPos_y*nc_x + nw_y*vc_x) - 2*dqb_q0_z*(diffPos_x*nc_x + nw_x*vc_x) + dqb_q0_x*(diffPos_x*nc_z + nw_x*vc_z) + dqb_q0_x*(diffPos_z*nc_x + nw_z*vc_x) - 2*dqb_q0_z*(diffPos_y*nc_y + nw_y*vc_y) + dqb_q0_y*(diffPos_y*nc_z + nw_\\\ny*vc_z) + dqb_q0_y*(diffPos_z*nc_y + nw_z*vc_y)) + dqn_q0_x*nw_x_a0*(dqb_qe_z*nw_x - dqb_qe_x*nw_z - dqb_qe_w*nw_y - 2*dqb_q0_y*(diffPos_x*nc_x + nw_x*vc_x) + dqb_q0_x*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_x*(diffPos_y*nc_x + nw_y*vc_x) + dqb_q0_w*(diffPos_x*nc_z + nw_x*vc_z) - dqb_q0_w*(diffPos_z*nc_x + nw_z*vc_x) + dqb_q0_z*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_z*(diffPos_z*nc_y + nw_z*vc_y) - 2*dqb_q0_y*(diffPos_z*nc_z + nw_z*vc_z)) - dqn_q0_y*nw_x_a0*(dqb_qe_y*nw_z - dqb_qe_w*nw_x - dqb_qe_z*nw_y + dqb_q0_y*(diffPos_x*nc_y + nw_x*vc_y) + dqb_q0_y*(diffPos_y*nc_x + nw_y*vc_x) - 2*dqb_q0_x*(diffPos_y*nc_y + nw_y*vc_y) - dqb_q0_w*(diffPos_y*nc_z + nw_y*vc_z) + dqb_q0_w*(diffPos_z*nc_y + nw_z*vc_y) + dqb_q0_z*(diffPos_x*nc_z + nw_x*vc_z) + dqb_q0_z*(diffPos_z*nc_x + nw_z*vc_x) - 2*dqb_q0_x*(diffPos_z*nc_z + nw_z*vc_z))'; 'dqn_q0_w*nw_x_a0*(dqb_q0_w*nw_x - dqb_q0_y*nw_z + dqb_q0_z*nw_y) + dqn_q0_y*nw_x_a0*(dqb_q0_w*nw_z - dqb_q0_x*nw_y + dqb_q0_y*nw_x) + dqn_q0_x*nw_x_a0*(dqb_q0_x*nw_x + dqb_q0_y*nw_y + dqb_q0_z*nw_z) - dqn_q0_z*nw_x_a0*(dqb_q0_w*nw_y + dqb_q0_x*nw_z - dqb_q0_z*nw_x)'; 'dqn_q0_w*nw_x_a0*(dqb_q0_w*nw_y + dqb_q0_x*nw_z - dqb_q0_z*nw_x) - dqn_q0_x*nw_x_a0*(dqb_q0_w*nw_z - dqb_q0_x*nw_y + dqb_q0_y*nw_x) + dqn_q0_y*nw_x_a0*(dqb_q0_x*nw_x + dqb_q0_y*nw_y + dqb_q0_z*nw_z) + dqn_q0_z*nw_x_a0*(dqb_q0_w*nw_x - dqb_q0_y*nw_z + dqb_q0_z*nw_y)'; 'dqn_q0_w*nw_x_a0*(dqb_q0_w*nw_z - dqb_q0_x*nw_y + dqb_q0_y*nw_x) + dqn_q0_x*nw_x_a0*(dqb_q0_w*nw_y + dqb_q0_x*nw_z - dqb_q0_z*nw_x) - dqn_q0_y*nw_x_a0*(dqb_q0_w*nw_x - dqb_q0_y*nw_z + dqb_q0_z*nw_y) + dqn_q0_z*nw_x_a0*(dqb_q0_x*nw_x + dqb_q0_y*nw_y + dqb_q0_z*nw_z)'; };result0 = cellfun(@strrep, result, repmat({'\\\n'},size(result)), repmat({''},size(result)), 'UniformOutput', 0); result1 = cellfun(@strrep, result0, repmat({'_x'},size(result0)), repmat({'.x'},size(result0)), 'UniformOutput', 0); result2 = cellfun(@strrep, result1, repmat({'_y'},size(result1)), repmat({'.y'},size(result1)), 'UniformOutput', 0);result3 = cellfun(@strrep, result2, repmat({'_z'},size(result2)), repmat({'.z'},size(result2)), 'UniformOutput', 0);result4 = cellfun(@strrep, result3, repmat({'_w'},size(result3)), repmat({'.w'},size(result3)), 'UniformOutput', 0);result5 = cellfun(@strrep, result4, repmat({'nw.x_a0'},size(result4)), repmat({'nw_x_a0'},size(result4)), 'UniformOutput', 0);result6 = cellfun(@strrep, result5, repmat({'nw.x_ae'},size(result5)), repmat({'nw_x_ae'},size(result5)), 'UniformOutput', 0);result7 = char(result6);arrayfun(@(x) result7(x,:), 1:6,'UniformOutput', 0 );
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